Riot just rolled out a new refer-a-friend system yesterday. I'm not really sure what the differences are between it and the old system to be honest. For the most part it looks like you just get small amounts of in game currency if a friend signs up through your link or enter your name (Ziggyny) and plays enough to hit level 10. There are some pretty substantial rewards further down for getting a lot of referrals but that seems like a bit of a pipe dream I would think.
The second way is to create a custom game. One of the options when you're forming the teams in a custom game is to add a bot to either team. This is how I ran my test yesterday. I added 4 bots to my team and 5 bots to the other team. These games have the same xp/ip as the Co-op vs AI penalties assuming the teams are balanced. The plus side here is you don't have to play with strangers if you don't want to. There's no pressure to win and you get some xp/ip at the end of the game.