You can get a 250 in there, but the belt will rub the side of the tire. Some people will grid to lip on the side of the tire down, as I have in the past. I'm running a 240 now, and just tell everyone it's a 250, you really can't tell the different.
I had a similar problem on my '06 K9. I replaced the rear tire with a Metzler instead of an Avon. Apparently the Metzler was a slight bit wider because the drive belt was rubbing on the tire. I found a 1/8" spacer on eBay that goes between the pulley and the hub to move the belt outward a bit. Works great. Moved the belt out just enough to keep it from rubbing on the tire.