You keep talking about “generating” pressure with the piston. That’s got me confused. Can it be done? Yep. I can think of ways to do that, involving hooking it up to the solenoid in reverse. But generally a piston does not generate air pressure, it uses it. The pressure generated at the non-pressurized end due to cylinder motion leaves via a vent valve, or the piston stops halfway, and we can’t have that now can we?
And when I say leaves, it’s virtually impossible to keep it compressed and use it again. You can slow down/stop the cylinder with it–see below–but even that use is tricky.
Your PSI estimate is correct, and a bit generous (never a bad thing). A=Pi*r^2, and with a 2-inch bore, r=1 inch, so A=Pi, which is about 3.14159 in^2. To generate 180 lbs of force on said piston, you need 57.296 PSI at a minimum, but 60 is a much easier number to play with, and a good overestimate, so we’ll go with that. The tough part is maintaining that PSI–I’d try to do the math for flow rates to maintain pressure in a given volume and all that, but it’s late and I don’t think I’m quite up to trying calculus at this point in time.
I’d look at using some of the FRC-type solenoids, such as the FESTO VUVG-L10-B52-T-M5-1P3-566458 or VUVG-L10-B52-T-M7-1P3, as those work pretty reliably. The SMC 3000 series was also used in FRC with a manifold, IIRC–some of the older FRC veterans might have a few laying around. SMC 5000 series should work also.
If I remember correctly, a single-acting solenoid causes the cylinder to default to one end or the other; tripping the solenoid causes it to move and untripping it causes the cylinder to return to the previous position. A double-acting solenoid has to be tripped both ways. So if you’re simply doing a quickish out-and-back motion, a single solenoid might be the better way to go; if you need to hold position for a while (and especially if you think there might be a power failure), a double-acting is probably better.
Bonus: some FRC teams have rigged a multi-position cylinder by attaching a single solenoid to the exhaust port(s) of a double solenoid, closing the single to generate pressure, and opening it to allow for full travel.
Just out of curiosity, what are you working on?