Is it possible to make a health regeneration ring that regenerates health when out in the sun as a vampire at stage 4 negating the effects of the sun damage?

Not without creating some sort of mod. "Restore Health" can't be enchanted on things.

No. Not in vanilla. The closest you can get is a home brewed potion of restore health. At high levels of alchemy skill and with good equipment, such a potion can restore 13 hp per second for 43 seconds. And they're pretty cheap and easy to make.