Is there any feat that allows wielding inappropriately large ranged weapons?
There are a few feats that allow one to wield inappropriately large weapons, but all of them are obviously intended for melee combat: Lighten Weapon, and Improved Lighten Weapon; Goliath Grip; Titan Technique, Titan Grip, and Titan Slayer.
Can any of these feats be used with ranged weapons as well? If not, is there any feat that exists to wield inappropriately large ranged (or thrown) weapons?
If you have those feats, you can definitely use a ranged weapon at least up to 4 size categories larger than you
Which would be Colossal for a Medium creature.
The rules behind this are kind of weird. Basically, it is unclear if projectile weapons requiring two hands to be used are considered two handed weapons or not. Fortunately, this ends up being irrelevant to your question. Either projectile weapons have a handedness corresponding to the number of hands they require to be used, or projectile weapons have no handedness. If projectile weapons have no handedness you can actually use any size of projectile weapon you wish, taking a -2 penalty to hit for every category away from your category the weapon's size is, since the rule prohibiting the use of excessively oversized or undersized weapons applies only to weapons with a handedness (weapons whose handedness is not light, one-handed, or two-handed don't change). If projectile weapons have a handedness, then these feats, which do not specify anywhere that they only apply to melee weapons, certainly apply to ranged weapons as well.
So, in any case, a character that has the listed feats or similar abilities can definitely use ranged weapons as if the feats affected their use, though the feats may not in fact do anything, in which case anyone could use such weapons by default. I've not had a GM choose the later interpretation once the situation was explained (people have thus far invariably favored the former, in my experience), but either is valid by the RAW.
Note that if you are using a firearm the handedness of the weapon doesn't change regardless of size, which used to mean that the rules explicitly allowed you to use a firearm of any size, but this has been FAQ-errataed to disallow the use of oversized weapons "just like non-firearms".
Further explanation:
Here's the most explicit rule that bans weapon use outside of normal handednesses (from the weapons section of the CRB but also found in the 'normal' section of e.g. Titan Technique):
The measure of how much effort it takes to use a weapon (whether the weapon is designated as a light, one-handed, or two-handed weapon for a particular wielder) is altered by one step for each size category of difference between the wielder's size and the size of the creature for which the weapon was designed. For example, a Small creature would wield a Medium one-handed weapon as a two-handed weapon. If a weapon's designation would be changed to something other than light, one-handed, or two-handed by this alteration, the creature can't wield the weapon at all.
So 'how much effort it takes to use a weapon' is defined to be its handedness and handedness is explicitly limited to three valid options: light, one handed, or two handed. When we upsize or downsize a weapon, we change its handedness one step and if our end result would be something other than light, one-handed, or two-handed than the weapon can't be used. Of the feats listed, Golaith Grip, Titan Technique, Lighten Weapon, and Titan Slayer all reduce the handedness modification for certain oversized weapons so that you could choose a suitable oversized weapon so that its handedness would be the handedness of a similar weapon of the appropriate size. If ranged weapons have a handedness (which must be light, one-handed, or two-handed, remember) then the feats would result in the handedness for an oversized weapon being an element of the set (light, one-handed, two-handed), so in this case ranged weapons benefit from the feats.
The fiasco with the handedness of firearms seems to lend credence to this interpretation as the designers, in their FAQ errata of the terrible, terrible firearm handedness rule stated:
Just like with non-firearms, a creature cannot wield a weapon that’s far too big or small for it.
Rather than 'just like with melee weapons'.
It could instead be argued that, while they may require one or two hands to be used to wield them, projectile weapons don't have a handedness, for example the CRB says:
Light, One-Handed, and Two-Handed Melee Weapons: This designation is a measure of how much effort it takes to wield a weapon in combat. It indicates whether a melee weapon, when wielded by a character of the weapon's size category, is considered a light weapon, a one-handed weapon, or a two-handed weapon.
Since these designations, in this viewpoint, only apply to melee weapons, ranged weapons have no handedness at all! When a game entity lacks a property and a rule tells you to modify that property, you ignore that modification. For example, if you cast Bear's Endurance on a Zombie the spell works just fine (i.e. the Zombie can be a valid target and the spell will come into effect normally) but the Zombie's Constitution score does not change.
If this is the case, then the handedness of projectile weapons can't change when you increase their size. You can certainly still get projectile weapons in different sizes-- the rules explicitly call out that every weapon has a size-- and you still take an accuracy penalty from that other rule:
Inappropriately Sized Weapons: A creature can't make optimum use of a weapon that isn't properly sized for it. A cumulative –2 penalty applies on attack rolls for each size category of difference between the size of its intended wielder and the size of its actual wielder. If the creature isn't proficient with the weapon, a –4 nonproficiency penalty also applies.
but since the handedness doesn't "[change] to something other than light, one-handed, or two-handed by this alteration" you aren't barred from using it regardless of the size. This, obviously, would also render your feats useless with regard to projectile weapons (since there's no handedness to reduce, either).
Despite the weirdness of this perspective, the rules do tend to go out of their way to call out the handedness of ranged weapons when relevant to Two-Weapon fighting in a manner that would seem to lend credence to this interpretation:
Thrown Weapons: The same rules apply when you throw a weapon from each hand. Treat a dart or shuriken as a light weapons when used in this manner, and treat a bolas, javelin, net, or sling as a one-handed weapon.
The "Treat x as y" language seems to strongly imply, but doesn't necessarily mean, that these thrown weapons at least don't have a handedness. Certainly the bola in particular never gives itself a handedness-compatible requirement in its description, despite the general rule that ranged weapons ought to do so. This would seem to indicate that at least some ranged weapons have no handedness, but the results of accepting that implication are extremely problematic (an Atomie, for example, could dual-wield Colossal Repeating Heavy Crossbows for example). Similar wording is used when describing how crossbows interact with Two-Weapon Fighting.
It's probably worth noting that the 'treat x as if it were a y' language doesn't always mean that x is not a y in practice as well as theory; for an example, the Forge domain variant channeling reads in part:
you may repair damage to metal objects and metal constructs as if they were creatures
While we all know that constructs, metal or otherwise, are creatures anyways.
Regardless of which of the two RAW-valid positions your group plays by (it's the first one. No one uses the second one. It only comes up when people start trying to argue why these feats and similar things don't work and put their feet in their mouths, but in that context it comes up quite a lot), a character that has any of these feats can wield a projectile weapon at least as large as if that projectile weapon were a two-handed melee weapon.
Extra notes from experience:
Just for the record, there is but a single official PFRG feat that I'm aware of (from the PFRG Advanced Race Guide) that affects the ability to wield a larger ranged weapon:
Goblin Gunslinger (Combat, Goblin)
You have learned how to fire the big guns.
Prerequisites: Goblin.
Benefit: You can wield Medium firearms without taking the penalty for an inappropriately sized weapon.
Normal: You take a –2 penalty when using an inappropriately sized weapon.
In addition, based on the "Normal" text of this feat, it seems to support the idea that a character can wield inappropriately sized ranged weapons with their associated penalties without need for additional feats or other class ability. In spite of this however, I'd recommend expecting table variation on whether a GM allows use of any inappropriately sized ranged weapons, even though it seems there aren't any official rules that place a restriction on their use.
Under the current core rules, there are no feats which allow you to use incorrectly sized weapons in the manor you are wanting. However there is a spell called gravity bow which allows your ranged weapon to deal damage as if it were a size category larger. You can then stack this with enlarge person. The problem with enlarge person is that the projectile resumes its original size once it leaves you, so you have to address that with endless ammunition spell or by providing correctly sized arrows in the first place.
So with this method you are able to increase the weapon dice damage by 2 categories which for bows should be 4 steps on the damage scale.
Some of the feats upon first glance may work because they refer to size category rather than to the handedness of a weapon but upon reading those feats in their entirety all of them reference the amount of hands required to wield a weapon based on its size which only happens with melee weapons.
There's no RAW feats in Core that will allow this (or in 3rd party that I know of), but I would cheerfully allow, even encourage, someone who was interested in this to write up the feat and present it for approval. Something like the Lighten Weapon and Improved Lighten Weapon feats that you cite above.
Yes, this means that the character uses up two Feat slots to wield a bow too large for them under normal circumstances ... so it's a choice, with both advantages and drawbacks. That way, it's up to the player to decide if that price is worth the advantages that it brings.
