Jeweler here. I’ve seen from other posts that what you’re asking is impossible, but I thought I’d share a little additional info/advice. I would not recommend a ring made entirely out of gemstones as they are vulnerable to breaks. While both of these gems are quite hard (amethyst is 6 on the Mohs scale, sapphire a 9), it is still risky, and if you’re wearing them every day they are going to have to stand up to a lot.

My recommendation would be to get custom rings with metal bands and regular sapphire and amethyst settings. You could do this in lots of ways (one sapphire and one amethyst on each rings, lots of little gems of each type, one sapphire for the ring of whoever’s stone that is and vice versa). Another idea is that metalsmithers hold classes on making your own jewelry, and I’ve even seen ones where engaged people can come in for a private class and actually make their own wedding rings. Look up metalsmithing classes near you and you may find something.