I stopped telling drunks I don’t know a song. If I tell them I don’t know their request, they act like I committed the worst crime imaginable. Instead, I usually just go straight into a similar song or a song by the same artist without saying anything. But if I say this song is better, or put down their request at all, they usually end up not tipping or walking off or arguing.
I am a street musician so my experience may be a little different then the bar experience, but I deal with a lot of drunks. Sometimes I tell them if they sing it, ill play it, and pull up the chords on my phone. Usually, they are too embarrassed to sing it or it turns into a hilarious and fun experience.
They like it when your in control, and for me, sometimes a sarcastic remark helps solidify the power and make light of the situation. Other times, It has almost gotten me into fights. So to wrap up, I usually end up not saying anything and tricking them into a new song that I know that they can sing along to. Or a song that I know they will like based on their request.