Eternity rings in both my and H's culture (Irish, Italian Maltese) are for the first born child.
Both my engagement and wedding rings are 18K white gold, so eternity needs to be the same, and tradition is 3 stones- one for mum, dad and bub. H wants them to be exactly the same size- which is hard to find. So I assume he will get it made, like he did my engagement ring.
ETA: it was originally first born boy, but got modernised.