If you don't have a dessert gooseberry, I can recommend Xenia. Don't believe any descriptions that say thornless, but they don't have that many. They are sweet enough to eat raw off the bush, but I cook them as well.
Another slightly different thing I have are 2 pink currant bushes. They are also pretty sweet, but do have a little bite, so more flavour than white currants, but not anything like as sharp as red ones, so are more easy to use in puddings.
If you have room for some posts and wires, the hybrid berries are also very productive. I have tayberry, loganberry and boysenberry and all are good. Loganberries are the tartest. Tayberries and boysenberries are sweet enough to eat without sugar.