Perhaps the answer is to try and educate the audience to the fact that all songs are a matter of personal taste? Not to be afraid to say that you would not wish to touch the song with a ten foot-bargepole and to give the reasons why. The song they want YOU to sing may be to their taste but it should not follow that it must also be to yours.

If you are not so brave (or wish to be booked again), you could inform them that the set list you have, is to your taste and you have rehearsed them so that they will be performed to the best of your ability. And that you hope that they will enjoy what you have prepared for them, as you have not got the time to prepare to requested song to the level of performance that will do it justice.

Or tell them to book Christy next time..............