noun
couple's ring; matching rings for a couple
Refers to matching or coordinated rings worn by two people as a couple; it is not the general technical sense of English "pairing."
wasei-eigo (Japanese-coined English), from pair ring
記念日にペアリングを買った。
We bought couple's rings for our anniversary.
二人で同じデザインのペアリングを選んだ。
The two of them chose matching rings in the same design.
婚約指輪 is an engagement ring, usually given for an engagement; ペアリング emphasizes a matching pair worn by both people.
指輪 is the general word for a ring worn on the finger; ペアリング is specifically a pair or set for a couple.
Wasei-English from English pair + ring, used in Japanese for matching rings for a couple; "pair ring" is not the usual English expression for this item.