The Revised Common Lectionary lists no psalm for Christmas Day itself. It makes up for it — somewhat mysteriously, it must be said — by offering three psalms for Christmas Eve 24th December, for three separate observances called Proper I, II and III.
For those (few?) who follow this pattern, which does not include Woden Valley Uniting, please read about these three psalms in the December 2020 Christmas post here.
Similar comments may be found on the individual pages for these psalms via the Index tab.
After waxing eloquent in the previous post regarding ancient music and early manuscripts, I could give you the 1734 Bach Christmas Oratorio, BWV 248. Lovely as it is, being in six parts for as many days of the Christmas season, it does tend to go on forever. Well, three hours, anyway.
Nothing to do with psalms? Neither is Christmas, but I got it in anyway — there’s bound to be a psalm text somewhere in those three hours. And the Fantasia is fine music.
The illustrated manuscript detail at left, from the Henry VIII Psalter c.1540, is definitely associated with Psalm 96. The words at right of the singers are, of course, the first verse in Latin: Cantato dominum canticu[m] novum. The small line over the u of Canticum indicates an abbreviation.
Meanwhile, here is something much more up to date. Listen to Psalm 96 from Australian psalm-singing band, the Sons of Korah: