YSK: The possessive of " you guys " is " you guys' "
Why YSK: because though "your guys/your guys'/your guys's" are so commonly used in this situation, they are entirely incorrect.
In Napoleon Dynamite, he asks "could I use your guys' phone?"
Grammatically speaking, he's asking if he could use a phone that belongs to their guys. What he means to say is "could I use the phone that belongs to you guys"...
a phone that belongs to \[a guy\]: \[a guy\]'s phone
a phone that belongs to \[several guys\]: \[several guys\]' phone
a phone that belongs to \[your guy\]: \[your guy\]'s phone
a phone that belongs to \[your guys\]: \[your guys\]' phone
a phone that belongs to \[you guys\]: \[you guys\]' phone #education