In our home game, I have a character that is wanting to pick up Leadership at level 7 and have some fun with a cohort. I have chatted with him about it and he is not intending to munchkin it as a healer, or crafter...just someone(thing) to hang around, help a little if needed, and add a bunch of flavor to his character and the party.
My question revolves around picking up a Monster Cohort. I am assuming you would generate its stats like you would a regular NPC cohort? SO you could have a Griffon with a 15 point stat buy and class levels?
As far as I've seen recommended you dont want the cohort to be as good as a PC, They should use the heroic npc stats table. I'd keep the griffon at standard stats and if he wants it to have better stats maybe let him pick up the advanced template instead of a class level
As it is a home rules game, it is up to the GM how to handle this. By rules as written, so long as a GM gives the okay, an unmodified monster could be used as a cohort - use the statistics as written in the bestiary for the average of the type of creature. There is a level equivalent that may make Griffons a bit prohibitive (considered equivalent to a level 8 cohort, so the PC should be 10+ level). After the initial equivalent level is reached, such a monster cohort gains PC class levels when it gains enough XP to level up (usually as fighter).
Knowing that he should be level 10 to have a griffon cohort, you could let him start right now with a young griffin. That's normally only a -1 CR template, so modify it by removing the size bonus to DEX. It's young a clumsy. When he reaches level 9, give it back the size bonus, and at level 10, remove the template - it has a growth spurt (or finishes the growth spurt that started at level 9).
Of course, he could always go with a temporary cohort for a couple levels then dismiss the cohort in favor of a griffon, but I like the first way better - it somewhat models the idea of getting it young and training it while it grows.