If you can round up a capable soprano to go with them, Hermann Zilcher's Marienlieder are excellent, though parts may be hard to locate. Check with WorldCat.
Also, a lot of SATB choral pieces work well when played by a string quartet--perhaps some of the Annunciation-themed pieces in the Oxford Book of Carols would fit the bill.
We have sung the "Biebl" Ave Maria with a trio on the second part and it has worked very well. It would also fit as the proper for offertory is "Hail Mary..."
If they have played together a long time, they will probably be able to give you a list of what they can play as prelude music and you can choose from there.
They could play one of the movements from Handel's Water Music along with the organ as a postlude.
Honesty, I would not have them play everything. I think that would be overkill.Think less is more.
Although I don't have any particular published composition in mind, an arrangement of the Basque carol "The Angel Gabriel from Heaven Came" (Tune: GABRIEL'S MESSAGE) would be appropriate.
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