"Prosperina" would be an entirely unrelated name to Proserpina (it would be a feminine diminutive of Prospero, in fact); but I agree that is does sound more euphonious than Proserpina. The latter sounds a bit too reminiscent of "serpent"; but the associations with the goddess of spring are nice. However, I definitely prefer the Greek "Persephone".
I first read this name as Prosperina, which I kind of prefer the sound of, and find makes more sense with the 'prosper' bit. Proserpina is such a goddessy name! I quite like it.
I love the way this sounds, but I can't really picture it on a modern person. Oh well, it's still one of my favorite names. I actually think it's prettier than Persephone, although I like that too.