There are various songs where they exchange rings as love tokens - e.g Lovely Nancy
"Come chagne your ring with me ,my dear,
Come change your ring with me.
That it might be a token
When I am on the sea"
There is also a South Wales song - a varient of the "She was Poor but she was honest" type that has a chorus
"Take this ring from off my finger
Take this necklace from my neck
Give it to that false young lover
To the one I loved the best"
Will post any more i can think of when I have more time.