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I thought Barnes used to offer a solid copper, flat-nosed, slug, but I couldn't find them. This is probably a fair round: http://www.selwayarmory.com/buffalo-bor ... of-20.html

or the Barnes 160 grain Hone Badger
http://www.selwayarmory.com/black-hills ... of-20.html

Gator hide is thick and tough, so expanding projectiles won't do a whole lot.

Personally, a Ruger Alaskan, in .44 Mag, in a chest-holster, with a hefty flat-nosed loading, would be a reasonable carry. Statistically, your odds of being attacked by an alligator are low. Those odds do increase, every time you meet them, and every time they meet other humans, and become less reluctant to eat, ah, I mean, "meet," you. Just like wild dogs. just like bears. Just like large cats...