"友達になってもらえませんか？” is perfectly fine.
"フレンドになってもらえませんか？” is also fine.
"お友達になってもらえませんか？" is okay in some contexts, but in other contexts, お友達 may mean "a real friend in our actual/daily life."
Usually, お友達 is just the polite version of 友達, but if "友達" is a specific word which is defined on that website, you should not say "お友達," which sounds funny.
These three literally mean "Could you become my friend?"
Other expressions would be:
”フレンドリクエストをさせて下さい。” "Can I make a friend-request to you?"
"フレンドリストに追加させて下さい。" "May I add you (as a friend) on the friend list?"
It depends on the websites on the Internet, and it depends on what "a friend" means in your case, but 友達になってもらえませんか or フレンドになってもらえませんか seems best for me.