Damsons are a lovely fruit and surprisingly expensive in Farmer's Markets!
I do Damson Jam and Damson Chutney and have a tip for stoning them.
Forget any recipes that say "skim the stones off the top of the pan with a slotted spoon" as the author has probably never actually tried it. Likewise don't bother "slitting the fruit around the middle and twisting to separate the two halves". Damsons are "cling fruit" and really, really hang onto their stones. Don't use an olive or cherry stoner as they won't release the stone either - I tried that one.
The technique I use is as follows and works for Jam or chutney... simmer the fruit as the recipe requires until the fruits have all burst and gone pulpy. Turn off the heat and allow to cool to a medium warmth that is comfortable on the hands. You will need some large bowls, a (preferably metal) colander and a clean pair of those yellow marigold gloves. Damson stones are small, hard and pointy!
Put the colander over the largest bowl or pan and allow any liquid to drain through for a few minutes. With gloves on, reach in and take a handful of fruit and stones. Squeeze your hand together, allowing the fruity pulp to escape between your fingers and try to retain as many of the stones as possible. Give a good hard squeeze, wipe the pulp off your closed hand with the other and release the stones into a nearby bowl then repeat. Do this over and over until you think you have got the vast majority of the stones out of the pulp. Use the back of your fingers round and round in the colander seeking any remaining small stones in the leftover thick pulp. Once you have gone over it thoroughly and come up blank, take a flexible spatula and "squidge" the pulp under the spatula against the colander to systematically check for more stones. Once you are satisfied, lift the colander and use the spatula on the underside and inside to save all the pulp and juice.
You should end up with a large bowl of pulp and juice,a small bowl of stones and a clean colander between the two. The plus side of this method is you are guaranteed to not have ANY stones in your jam or chutney. The downside is that you will have thoroughly pulped the fruit so you won't get any chunks of fruit at all. If the alternative is chunky jam and a trip to the dentist because of a forgotten stone, I'll take the colander method, thanks.
As for recipes I can offer the following...
Damson Jam : 1.1kg damsons, 568ml water, 1.4kg sugar makes 5 jars jam.
Bring fruit and water to a boil then turn off heat, cool and remove stones. Add sugar, reheat, boil briskly for 5 mins and check for setting point. Damson jam should set well. Pour into hot jars and seal.
Damson Chutney : 1350g damsons, 1200g white or cider vinegar, 450g apples, 3 large onions, 450g dates or vine fruit, 450g dark muscovado, 450g light muscovado, 3 cloves garlic, 2 tbsp salt, 1 tsp ground cinnamon, 1 tsp ground cloves, 2 tsp ground ginger.
Simmer the damsons with 300ml of the vinegar until pulpy and remove the stones. Add rest of vinegar and all other ingredients and bring to gently boil. Lower heat to a very low simmer and reduce over 2-3 hours, stirring frequently until very thick and leaves a cleared trail behind the spoon on the bottom of the pan. Do not allow to stick. Pour into hot jars and seal. Makes 6-7 jars and takes 1 month to mature.