To be sure, do you have the model# of your compressor? This would help.

Essentially, the Rings don't have to be staggered in an EXACT location, as long as the gaps ARE staggered you're fine. So if you have 3 Rings, just stagger them so that the gaps are 120 degrees apart and you'll be fine.
As for compressing the rings, if you can't use a ring compressor then take some plumbing strap (has small holes in it) and compress this around the Rings with vice-grips, then push the Piston and Conrod down into the Cylinder.
This pump probably doesn't have a removable Cylinder as the Cylinder and Crankcase are one cast aluminum piece, with an oil pan. If this is the case then you HAVE to install the Piston/Rods from the top of the Cylinder, then bolt the Conrods down onto the crankshaft.

Hope this helps!
- MTR

Thanks for the info...this model is very familiar to me, it's the old, old "VT" series pump which Campbell Hausfeld manufactured for Sears.
This is going to be a typical Ring installation, then. You'll end up compressing the rings and having the pistons and rods already installed on the crankshaft.
You'll use the steel band to compress the rings on one Piston first, then shimmy on the Cylinder. Make sure you have one Piston at the bottom of it's stroke and the other at its highest point. Obviously you're going to start with the higher piston, shimmy the cylinder on, then start with the second Piston.

I've included a nice .PDF document that shows you how and gives you a visual. The model of the pump isn't the same but the method will be exactly identical.

Again, good luck and I hope this was of some assistance!
- MTR

I believe the part# for the "Valve Limitor" is VT021500AV at $4.83 each
www.mastertoolrepair.com/valve-limiter-vt021500av-p-17791.html

The only info I have states it's 18 gauge steel.

I'll double check with the manufacturer and get back to you. I'd like to confirm this is the right part.
-MTR