I know the OP specifically asked about center fire rifles, and my vote was for the .22-250 and it still is, but I wanted to also say that my Marlin model 25 ( I think it's a 25 ), in .22WMR is a decent little varmint rig. Bolt action, synthetic stock, mine has a pretty decent scope and a good bipod. I'd like to slick up the trigger a bit if it can be done without sacrificing reliability.
With today's improved ammo that rig makes a nice sub-150 yard critter killer.
I know that some folks think the .22 mag is an affront to weaponry, but for some reason I've always been a fan. I have a couple of rifles and at least two revolvers chambered in it, and they have each served me very well.
My little Single Six has dropped many a pesky porcupine with one shot, and my Marlin has taken a couple of large coyotes from a bit over a hundred yards. Both were eating from a gut popsicle out on the swamp near my place. The first one dropped dead on the spot with one shot through the lungs. The second one took off when his buddy was shot but came right back. He went right down with a shot that severed the spine right below the neck.
I'm in the heavy forrest of the northeast, so that's about as long a shot as I'll ever take.
It's relatively quiet, no recoil to speak of and packs a bit more punch than a .22lr, plus I happen to be sitting on a few thousand rounds that I bought before the great .22 famine.
Anyway, just my rambling 2-1/2 cents....