I wrote this as a comment elsewhere, and thought it perhaps worth reproducing:
You can get congregations to sing new music, but it takes a bit of work and cooperation from your organist/music director/whoever.
5) Try to make sure the first and last hymn or song of a service are tunes that people do know. I was taught that the first and last notes a musician plays will be what most people remember; this is also true of liturgy, and familiar, well-loved hymns at the beginning and end of a service will be less disorienting.
6) If the music is something people are going to be singing a lot (say, a hymn for Lent with different verses for each Sunday, or a congregational Mass setting), or if it's a bit difficult (syncopation, changes between triplets and duple quavers, awkward leaps in the melody, changes in harmonic rhythm and so on), it's worth offering a brief rehearsal at some point so people can go over the tricky bits. Try to make this short (ten minutes is plenty) and don't expect to get things perfect. Make sure it's at a time people can attend -- after a service is usually best.
7) Try not to introduce new music alongside changes to the general format of services, and don't introduce too many new things in quick succession, especially if it's a long time since the congregation has had to sing anything new at all.
1) If you have one, see if you can get the choir (or music group or what have you) to sing the new tune (possibly to old words!) as a Communion hymn or an anthem a few times.
2) In the weeks running up to the use of the new tune, ask the organist/musicians to play it as part of the processional or recessional voluntary (whichever people are more likely to listen to), or even a short verse after the reading of the Gospel if appropriate.
If people have heard it a few times, they’ll find it much easier to sing.
3) Having sung the new tune, don’t abandon it; use it again in a few weeks time, if possible. (Again, you might want the choir to do this with different words.)
If copyright allows, I also find it helps to include music notation for the melody in whatever the congregation are reading from. At our church we have a fair number who read music “a bit” but don’t sing in the choir, and between them and the ones who pick up tunes quickly by ear, it isn’t so terrible.
4) Try to get people to sit close together. If you are Anglican this is probably the hardest step, but it really does help.