I don't know. I suggest a Jostaberry. Like big blackcurrants. Grows like topsy. Strikes cuttings like you never saw. Makes good mixed jams and sauces. One thing not liked is drought but stays alive underground for a second revival. A cross of blackcurrant/gooseberry. Why not try it?

Sounds like insects are the cause of the stickyness.
Is the stickyness on the fruit or the leaves? If so according to www.gardening-resources.com/pests and diseases of blackcurrants , suggest dissolve 1 pint of lime sulphur into 14 pints of water .But you must do this when the leaves are at the size of an old 10p