Mulberry season was my favorite time of the year for carp. My go-to fly was just a bunch of thin strips of foam (maybe matchstick thick) tied in at the middle of the piece at random places and angles along the hook shank. If you can find a piece of foam in a color you like, great, otherwise get white and a magic marker. Green stem optional. I used white more often than not and just colored them in various shades to really "match the hatch."
I tried a few other things like wrapping some foam around the shank (think like rolling onto a paper towel tube), gluing the layers together, and using thread as the divider to make better "segments" of the berries, then shaped it with a razor, but frankly everything else was more complicated, time consuming, and wasn't any more effective. I also tried adding a bit of lead to be able to really get it to "plop" and sink a few inches before floating just like actual mulberries falling. But again, it really just added time and didn't seem to make it more effective.