Let me start by saying that there are many ways to get the ring out of a snare drum, the best and most effective is to tune it out.
There is in some cases that this is not possible, so what most would do is put an O-ring on the top head and that would probably
solve your problem. The only problem with that is now you have a drum that is most likely over muffled. What I have found with my
experience working with some of the greatest drummers of all time, i.e. Jeff Porcaro, Terri Bozzio, Vinnie Colauita, to name a few.
The most precise yet inexpensive way that will allow you to get the perfect amount of ring out, and what I used for years with these great drummers, is duct tape, yes good old duct tape. Cut a piece about 4 inches long, roll in inside out, sticky on outside, and place it
anywhere on the surface of the drum. You now have perfect control of how much or how little ring you want in your snare.