I am originally from SD and have folks there. You shouldn't have a problem with the P'dogs, they are in great abundance. Most times we just take out .22lr's (10/22 or marlin 60) and shoot from 50 yards or so. .338 win mag works too
but I only did that once (got too expensive).
Anyway, check the regs I think you need an out of state permit as well (i was always in state because I was always in the military and home of record is SD so never had to get out of state permit).
Just ask the ranchers in the area for permission. Best bet is to go to one of the smaller mom and pop cafe's or taverns and ask around. You will get guys coming up to you to ask you to take out some p'dogs for them. Also, might want to try the pierre area. tons of federal land and lots of farms and ranches that will give you open access.
JOE