Simple things to do with very tart plums?
Tart fruits work well in jellies and jams, or as candied fruit. These all allow you to vary the sugar content to get the level of sweetness you want, plus you don't have to worry about botulism as much.

You could also try a fruit-infused brandy: cut fruit into slices, and layer fruit/sugar/fruit/sugar into a tall lidded jar. Cover with a spirit of your choice, usually vodka, although a milder brandy or white rum also works. Let this sit for several weeks to infuse, strain, and use as a flavoring in cooking or as a mixer in cocktails (or just drink it).