Here are my suggestions. Remember: these cost you nothing and they may be worth what they cost.
1. Pray - kinda obvious (but see above). God can work miracles or He can just transfer your bad singers (or their spouses) to another city. He has a lot of tools in His bag.
2. Make a recording of your singers. Now, be very kind when you play it back.
3. Find an example of the sound you are looking for on CD and play it for them. Maybe they just don't know how "off" they are from the mark.
4. Explain what kind of sound you are hoping to get from them and let them know (in the kindest way) that you're not going to be happy until you get it. They need to know that you're serious about this and aren't going to give up.
5. Show mercy. James 2:13
because judgment without mercy
will be shown to anyone who has not been merciful. Mercy
triumphs over judgment.
6. Verify that the monitor system is up to par and that they can hear themselves.
7. Maybe give them designated times to sing and times not
to sing. That way, you can limit the effect of bad vocals to the part of the song where they'll be covered by the congregation (well, we can hope).
8. Work with anyone who has a good heart and is willing to learn. Try to develop a relationship with these people (invite them to a cookout, etc.). Warm up to them and try to get them to see that we are servants, not rock stars. We should all be willing to improve and capable of benefiting from constructive criticism.
9. Maybe bring in another excellent backup singer (as a guest) and stand them next to the flat singer so he/she can hear what his/her part is supposed to sound like.
10. Bring them down in the house mix but do not turn them off.
11. Give them all some time off. This allows you to re-establish the musical direction without distractions. Maybe bring them back one at a time, allowing you to concentrate on getting each one to blend as much as possible. Who knows? Maybe they'll decide they like arriving later and not going to rehearsal.
12. Pray some more.
I hope this helps,