M.L.
I worked at a fine jewelry store and women replaced their rings all the time. Women also replaced old/fake/lost stones from their original wedding rings all the time. Any jeweler should be able to do this no problem.
You can either replace the diamonds, which could be cheaper than buying a whole new ring. Or you can get a new setting, a new center stone and use the original stones in something else.
If you love the ring, I would just replace the stones. You can use a cubic zirconia which will save money, but the brilliance of the stone may look a little off when compared to the actual diamonds around the setting since they won't be as flawless and bright as the cz.
There are conflict free diamonds available if that is important to you. Also, Herkimer diamonds (quartz crystals) are mined in the us and are a little less expensive. You can always order loose stones and take the stone and the ring setting to the jeweler to have them put together.
http://en.wikipedia.org/wiki/Herkimer_diamond