As long as theres a bit of ring to begin with (meaning the drum wasn't overly dampened when recorded) you should be able to emphasize the ring by using a healthy amount of compression with a fast release. Just let the comp stomp on the initial attack of the drum (the hit itself) and jump off immediately afterwards, so you can pull the decay (ring) way up. I normally use compression with a semi-slow attack and slow release to kill unwanted ring, but you can reverse this (quick attack and slow release) to emphasize the ring if you wanted. You may want to even use a separate compressor just for this. I've used a dedicated compressor plug just to kill unwanted ring before, and a separate comp to get the main sound I was after.
If that doesn't work, and you don't want to blend in another ringy snare sample, you could maybe get or record a sample or samples of striking one of those big plastic alhambra water cooler jugs (crazy, I know) and triggering that and blending it into the background behind the snare. I would highly recommend the compression trick first though.
Oh and also, don't put too much reverb on the snare, as that is actually a good trick to mask snare ring sometimes.