Large 2 BR For Rent (http://siouxfalls.craigslist.org/apa/2766102732.html - broken link)
3 Bed, 2 Bath Home. Blocks from parks, schools and more! (http://siouxfalls.craigslist.org/apa/2801821835.html - broken link)
Those didn't specify how many pets, so may be worth a call.
Also, (if you like mobile homes) you could check into these:
sioux falls apts/housing for rent classifieds "mobile home" - craigslist
I've had my best luck with mobile homes allowing pets, but maybe you'll find different. Hope you find something