For my Divided States variant, I drew the map using GIMP. You can download it for free at gimp.org.

However, that's not all there is to making a variant. I found the following tutorial very helpful because it outlines the general steps to take when making a variant digital and compatible with the WebDiplomacy software:
http://forum.webdiplomacy.net/viewtopic.php?f=25&t=432&sid=9da291710276051efbee8d2a2a5af329

Basically, the WebDip PHP code uses a map with one color per land territory to properly color in the map. The tutorial I linked to outlines how to do that. Once the program reads the map colors, it then overlays that map with an image of your SCs and names.

Once you have the PHP and name maps completed, send them and any custom code you created for your variant over to a variant lab. Basically, there is an interface that allows you to set the coordinates of a territory as well as what territories it is adjacent to without having to write it all in PHP. It's a real timesaver. As of right now, the only active lab I know of is this site called lab.diplomail.ru, but Oliver over at vdiplomacy.net may add the lab feature back to that site.

I'd suggest looking through the forum over at vdiplomacy because many people there have had the same questions as you.

I'm curious to see what you come up with!