Recently there has been some effort at making variants. There have been gunboat and similarly simple things in the past but Sleepcap and jayp have been working on their own servers (I think both are also translations) and sharing the patches around on the dev forum:
http://dip.xbsd.kr/boards/352/
http://forum.webdiplomacy.net/viewtopic.php?f=11&t=319
Making a basic (same-rules) variant from webDip isn't hard technically; Sleepcap pulled it off very well without any PHP/MySQL know-how, it's mostly just updating territory records, border links, and map images, though it takes some time and effort of course
What's more exciting for us is jayp, with more tech ability, has been adding some patches to Sleepcap's new variant data and maps which let normal and South-American run on the same server, so it could come much sooner than I had planned
These are for 0.82 though, and a set of patches for a Korean(?) server don't (necessarily) mean it'd be an instant, neat extension to the official code here, but it looks well made and once you've got two variant options on one server adding more gets much easier.
So I can say webDip variants exist and they'll be here too, much sooner than I had thought :-)