Rules as written: No
Though you won't see any rule saying "you cant do this", Pathfinder works with rules that say "you can do this". If it doesn't say you can do something, then you can't do it or will have to ask your GM. It's a game of exceptions. We have general rules, and exceptions to those rules, which in their turn have their own exceptions and so on.
The weapon must deal damage. Even if said damage is reduced to zero by other means (ie: damage reduction or stoneskin).
"Contact" is ambiguous because it could then be used with touch attacks (not allowed), or weapons that deal no damage, like nets (again, not allowed).
Why aren't you allowed to use them with touch attacks? Because touch attacks deal no damage that can be improved, The same is true for a flaming net, though iv seen people rule that a flaming net would burn every turn that the target is entangle, and also have seen it being ruled that the new wielder of the weapon is the entangled target, who can turn it off again.
A net also never gains the extra points of damage when you make it magical, just the attack bonus.
Weapon enchants are all a little ambiguous and vague, even in Pathfinder Society, so you will have to talk to your GM about what you can or cannot do before investing your money on them.
But i know of at least one item that allows elemental damage with touch attack: Deliquescent Gloves
So, if you were allowed to cause flaming/frost/shocking/corrosive damage on touch attacks, you wouldnt need to specify it when you have one item that allows using touch attacks to deliver the special damage. And we would see a lot of people with +1 weapons full of enchants attacking touch AC and dealing a lot more damage, they all would focus on two-weapon fighting and disregard their attack bonus completely, because even a dragon has a touch AC no greater than 12.
The rules of combat state that you hit the Armor Class to land a damaging blow to the target. A touch attack is a special exception to this and isn't a damaging attack.
Let's read touch attacks:
Some attacks completely disregard armor, including shields and natural
armor—the aggressor need only touch a foe for such an attack to take
full effect. In these cases,
So we can see that for touch attacks to work, the rules must specify that all you need to cause damage is land a touch attack on your target, like happens with touch spells (Example: Shocking Grasp), which is not the case for Flaming/Shocking/Frost/Corrosive, Bane, +1/+2/+3 and so on.
Another exception is the Gunslinger class, that can hit with guns on a ranged touch attack if the target is within the first range increment. Gunslingers, then, could use flaming effects on their weapons even with touch attacks.
So, let me sum this up:
All weapons must hit the target's AC, not their Touch AC, unless specified otherwise
(like a net needing only to hit touch AC to entangle someone).
If you somehow managed to convince your GM otherwise, be prepared for a s***storm, with monsters grappling you with touch attacks, draining levels, causing diseases, etc.