I use iron sights on small game such as squirrels and rabbits. Oh, I forgot to mention that the iron sights are sitting on top of my Ruger Super Single Six 6.5 inch stainless revolver. Very challenging, but very rewarding as I have had good success hunting with this gun. I hunt with the 22 magnum cylinder.
With a little practice, you should be able to shoot the old bushytails with a good 22 rifle using iron sights also. I used to have fun shooting them through scoped 22's, but wanted something a lot more challenging. I would rather bring home one or two with a iron sighted handgun than to bring home a whole bag with the scoped rifle. It sure does help your woodsman skills when you have to get closer for a good shot. I can consistently hit head shots on squirrels within 25yds with the Ruger, although I have to wait for the still shot in order to do so. Otherwise, a body shot on a moving one is also a good shot for me.
You will need to try several different types of ammo and see which one your gun groups the best. It's kind of funny, but 22 caliber firearms are also picky about which ammo they like the best. Make sure you are shooting from a sturdy rest (such as a sandbag), or else you will be testing your accuracy and not the rifle's.