THe auction place out past Dalry on the road to Irvine had signs up that it was doing a land auction - dunno when it is tho - think its called morrisons or something like that (I was driving, didnt get long to read and came home another way)
Check out local riding schools.
Some may have a secure indoor or outdoor arena that you could hire out by the hour. Might do the job till you find a suitable piece of land.