One trick that has worked for me is to offer the audience, or people who want to make requests, a songlist to choose from. That way they will always pick songs that I know instead of stammering around asking for songs I don't know (endlessly). I can't play everything and wouldn't want to play it if I did so guiding the audience to where I want them to go seems to not only save us both frustration but it adds to my tip jar as well.
I actually think it's a wonderful way to do it. Trying songs that you don't know... well... you might get through it but you might just suck. I hate that, lol! I also hate to hear somebody absolutely butcher a song. One verse/chorus, ok, quit and laugh it off. Or the whole song is fine if you know it and don't suck. But if you don't know it... a whole song, spare me, please!