Emeralds are bad choice for a ring that's designed to be worn daily, as are opals, pearls, and other soft stones.
Rubies and sapphires are good, because they're pretty durable. Sapphires come in all colors but red (because red corundum is ruby), including clear. If you're shelling out bucks for an engagement ring, you can get a good quality ruby or sapphire and still generally pay less than you would for a diamond. White sapphires have been a historically popular substitute for diamonds.
There's at least one company out there that sells "green" engagement rings, made with recycled gold and synthetic diamonds. (The synthetics they use are the yellow ones, but the rings are pretty cool looking.)