You can actually more or less blame Britney Spears for that one, actually. Prior to 2001 some of the major national rental fleets still had manual transmission cars, but after this well publicized bit of stupidity they were all removed. The only major national chain that still has any manual cars at all (that I know of) is Hertz, and that's their Hertz Mustang GT from the Fun Collection.
However, there are many smaller regional or local chains that sometimes offer manual transmission cars. You may also be able to find one at the Rent-A-Wreck chain. Caveat emptor there, though, and there are significant upcharges.
Oh dear, one more reason to dislike her.
Well, seems like it will be easier to buy a cheap Miata and sell it before going home.