An eternity ring is the traditional ring for giving at the birth of the 1st born. It is worn on the wedding finger along with wedding ring and engagement ring. Therefore it might be worth your while checking to see if its just a straight band you need, which will be easy enough to purchase. Or if you need to get one fitted around the rings already there,if they are wavy or have any other up and down design, in which case you may have to go and get one especially made, in order for it to fit snugly.
Hope that makes sense.!