Red currant, raspberry and gooseberry all will produce a reasonable crop in shade. How much better they'd be in full sun I don't know. In the wild gooseberries crop up as an undershrub, raspberries are more often open to the sky, but the UK centre for raspberry production used to Blairgowrie (Scotland) so one would assume they haven't got very high requirements for sun. As another poster says, redcurrants need bird protection.

I've never grown blackcurrants so can't comment on them.