Get a heavy snare drum with a head coated in white. This should cut down on a ringing sound. This is standard for a snare drum, even if you have different heads for the rest of your drumset. A thick bottom head can help as well, though this head should not be coated.
Use a ring muffler. This can either be a clamp mechanism or something that lays on the snare drum itself. A common method is to cut a ring out of an old snare drum head around an inch wide and lay that on the snare drum. An even cheaper method is to stick a piece of duct tape on the top or bottom of the head.
The website drumjunction suggests venting the snare. This involves drilling holes in the side and creating a gap in the shell. This lets the air out of the shell faster and makes the bottom head louder.
Check the snare on the bottom. If the snare buzzes a lot, lay the snare flat against the drum. Always replace a broken snare.