As a direct answer: You probably aren't going to find one.
Now, to explain why:
Pathfinder's not designed for single-PC (also called "one-on-one" or "twosie") play. Sure, the mechanics support it, but encounter and spell design go way off track. Any ability which would normally incapacitate a PC in a regular party can effectively become a "save-or-die" spell, which in turn becomes a TPK. Thus you need to choose between not using these spells and abilities, or risking the PC losing on a regular basis (whether or not the game survives a TPK is a separate issue).
Ironically, this is actually the opposite of the usual problem in Pathfinder, where a single big monster is put up against 4-6 PCs. One good sleep (or level-appropriate equivalent) and the fight is over.
Additionally, the action economy (how much you can do in a given round), which normally favors the PCs, swings towards favoring the monsters instead. That means that groups of monsters can easily overwhelm a single PC simply by having more of them.
Finally, certain monsters are easier to deal with via spells, or ranged attacks, or getting up close and meleeing, and no one character can be good at all three. So even if the CR is adjusted to account for save-or-lose abilities, the difficulty of a given monster will differ based on what your single PC can do.
These reasons lead to two conclusions:
- Monster CRs will not be accurate. Not that they always are now, but certain powers will seriously boost a CR compared to regular.
- Monster groups will scale up CR faster. Two monsters is probably handleable. Five will be much harder, even if they're individually weaker. So the scaling needs to be recalculated as well.
Now, what can you do about this?
There are several options to make this work for you - not all of them are practical, but I'll at least touch on them.
- Find more players. Obvious, but worth mentioning. There are plenty of reasons not to do this (no one around, want to just play with a spouse, etc), but if you can recruit even one more player, there's no longer nearly the same level of difficulty compared to normal.
- Play a different game. Also obvious - there's plenty of systems out there which do support single-PC play better. But if you're specifically wanting to play d20/Pathfinder, then this is a non-starter.
- Have a bunch of extra PCs, GMPCs, or NPCS. This is probably the best general-purpose solution. Artificially inflating the number of people fighting on the player's side will serve the same purpose as finding more players, without actually needing more people. However, each variety of this has its own considerations:
- Extra PCs - This involves having your player playing 1-3 "extra" characters on top of their main one. This brings the game much closer to its origins as tabletop wargaming, with your "army" of monsters against the player's "army" of PCs. There's nothing wrong with that, but it may be a different feel than regular combat, because the player is manipulating multiple characters instead of identifying with just the one. Out of character, there won't be the same level of party interaction that there is normally, unless your player is really good at roleplaying with themselves. This is the easiest solution for you.
- Extra GMPCs - Same idea as the last one, except you as the GM control the other PCs. This preserves the normal feel of combat for your player, and gives them someone to RP off of out of combat, but it puts an extra burden on you, and you'll be controlling both sides of every fight. This is probably the best solution for playing with a young kid.
- Extra NPCs - Superficially, this looks like Extra GMPCs, except here the NPCs aren't very useful in combat themselves. A bard who always uses Inspire Courage. A cleric standing by to cast healing spells every turn. Things like that. Unlike a GMPC, they don't need to be fully stated out. Instead, just have a list of abilities they can use (mostly on the player), and let the player choose which one to call on each turn. It might be worth borrowing an idea from 4e and having at-will (or constant), 1/encounter and 1/day powers for each. You can even have a whole stable of them, and just pick a few to take with for each mission. (This is kind of like Pokemon-type games, now that I think of it.) By providing these supporters, you avoid the insta-fail nature of single player play, but don't require the overhead of either of the other two methods. This is probably the best one for slightly older kids.
- Special pre-made adventures. Again, two sub-types here.
- There are companies which specifically make Pathfinder-compatible one-on-one adventures (example), which are designed to avoid the problems inherent in this type of game. I can't say how interesting they are, or how well they work, but they do exist.
- Alternatively, you can play in a world such as XCrawl where "adventures" are not "real". In XCrawl specifically, D&D is a televised blood sport in a otherwise-relatively-modern setting (with magic). So you could spin it as a game show where whenever the single player loses, they're picked back up off-stage, have a "life" deducted, and sent back in. This still has all the balance issues from above, but it provides an in-character framework for surviving even the worst death and trying again. (You don't need to use XCrawl specifically, but use the concept of "it's just for TV.")
Hopefully, some of that helps.