I stopped telling people I don’t know their song request, especially if they are drunk. If I tell them I don’t know it, 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 ask them to sing their request and I will play it. Then I 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 I am 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 trick them by playing a song I know that they can sing along to by the same artist. Or I will go straight into a song that I know they will like based on their request.