"convene" IS used, but with the completely different meaning of 'coming together' (for a meeting, as in "convention"). The OED does say its origin is "late Middle English: from Latin convenire 'assemble, agree, fit', from con- 'together' + venire 'come'", but I don't think it's a valid translation for 'conviene' anymore.
I'd agree as that is the common usage of convene in modern days (in my last post you'll see I said it's not used in the sense of convenience) but at the same time I'd like to think that words can and should still be used for older purposes when derived words are still used for the same sort of meaning, i.e. "convene" with "convenient/ce".
Remember, language isn't static, unless we let the dictionary bureaucrats tell us how to talk :)