oh, I get it, Dave. I would think the handle/latch would be conv-specific, cuz, well you know BMW. Why not find a glovebox off'a ebay, but make sure you specify must be conv,etc. I just checked ebay (keywords: E46 glovebox), & many sedan boxes came up, but a couple of ci's showed up. Didn't specify cabrio, though. Prices were cheap...why not give it a go, then bring both latches to key guy,...or if u prefer NOT to do that, go to key-guy 1st w/ dilemma to ask if it's be beter if he ad 2 latches/tumblers to tinker with to code it. I'd be sure (if go ebay) to make sure glovebox is same color (of course), cabrio (to be careful/preventative), & within the same year by 1-2 years (ie. if yours is 2004, lee-way 1-2yrs both ways).
That's just my 2 bits. Good luck Dave.