I've used Zymol HD Cleanse to get overspray off of hard plastic trim but I don't know if that would work on rubber or not? Might be worth a shot?? That's a good one...and you know we have to ask...???!!
3M™ General Purpose Adhesive Cleaner. It is pretty strong stuff. I've used it to take cosmoline, tar, etc off of solid materials but it should work on tires too. You might double-check with you favorite body shop first though. http://www.3mestore.com/62478765092.html?WT.z_xsell=1&WT.z_refSKU=62466749306
The 3M stuff is an excellent solvent-based cleaner, but I'm not sure if it's advisable to use a solvent on a relatively soft material like your tire sidewall. If you have a whole lot of paint on the tire, might be easy to spend a few bucks to have the tire flipped on the rim and re-balanced, depending on whether the tire's unidirectional or not. If it doesn't come off with some scrubbing (a stiff-bristled scrub brush perhaps? don't scratch the rim...) perhaps pull the wheel off the car, completely deflate it without breaking the bead, and try pushing on the tire edge a bit to get the sidewall to flex some, and maybe break up some of the paint's adherence to the tire. You can't drive on it deflated, that'll kill the tire, but a little light flexing would seem unlikely to damage anything. You might pose that question to the Tire Rack folks as well, they might have a suggestion.
Thanks for the replies. I did manage to get most of it off. The rest will take a little more time and effort.