I have used Remo Coated Ambassadors and Aquarian Satin Coated on m Pearl 3x13 steel snare and it works fine. I currently use an Aquarian Modern Vintage Coated on my 4x14 Tama Starclassic Maple snare and it sounds good--crisp, nice volume.
If you want to mute the ring or lower the dynamic options, you can try Remo Controlled Sound heads, reverse dot, etc. I've heard Aquarian Jack DeJohnette heads helped to control ring in snares.
Of course, you can always use the old trick of putting your wallet on your snare near the rim or use Moongel or the like. That will help give you a nice, tight, James Brown funk snare sound.