How to fix relationship with cousin dumb?

My 12yr old cousin usually comes to visit every weekend or so and took my MF game awhile back and would come back as if it was his and he finally gave it to me after telling him but then i guess i misplaced it one day and i saw him with a minecraft game and stole it back which was in his backpack.
I really thought it was mine and after i heard him tell my brother he was going to play MF on my xbox i asked him how without the game and basically he accused me of stealing and we went into a screaming match about it and how he had bought it and i probably lost it and he ended up in tears cursing me out.
And telling me how much he F** hated me
finally i told him ok you can ask me if i can have the game thats the only way you will get it and no this that and my brother saw me buy it
long story short he has been known for lying mostly encouraged by my brother for his behavior. Thats why i strongly believed it was mine until he left angry to be dropped off at his house.
Well i found the game now i have 2 MF's lol and now i feel so bad and i wished i had just given it to him or that i hadnt had stolen it from him and i'm sure hes going to tell his dad which is going to be very embarrasing i don't even use the game i only bought to play with them
so i have no idea what to do and i don't think hell be coming back but his dad will he comes almost every few days
i wanted to message him via ps3 to apologize but that seems awkward since hes 12.im not going to admit that i fnd my game