The 271 and 291 are homeowner saws, I guess not worth China's time to make cylinders for. My buddy had a scorred 291 he got for a project saw. We tried for six months to get a used cylinder. I finally honed out his old cylinder and buffed it with scotchbrite, there were still score marks and worn areas, but I threw a new piston and ring on, gave it a try and was surprised it ran and has been running for a while now. If you are dead set on rebuilding yours, you might see if you can find a scorred cylinder you can get for cheap and try to buff it out and see about getting it to work. I even went as far as to order and $11 Farmertech 290 cylinder...but the bolt pattern didn't match up.
It might be more cost effective to buy a new saw and part out the old one and sell the good parts on e-bay. I just bought the lever control for my 271, so there is a market for those parts. Just had another thought, if you have a dump nearby where you can look for thrown out saws, you might find one there over time, I have found several saws at my dump to include a Stihl 046, Husky 272 and 2100CD. They need some work, but for the most part the expensive pieces of them are in good shape.
If your son decides to get a new saw, look at the MS 261 (either Mtronic or carb version), it has a 1/2 horsepower over the 271 and a plethora of aftermarket parts. The Mtanlo piston and cylinder kit for mine ran about $50 from Amazon and has been working great. Plus you can use the bar and chain from your 271 (you might be able to talk your dealer to selling you the power head only, saving some money - where I worked, we used to do that for people who already had bars and chains for their saw) on it or convert it to run 3/8 chain.