i'm just making things up so i cant point you to a website or anything

but i'd layout one of the rings, then (i've never done this but i've seen someone suggest to someone else to do it) transfer the UVs to 7 other rings and move them around so that all 8 rings have UVs in different coordinates.
then id transfer the UVs from those 8 rings to the rest of the rings. 8 should be enough to take out any sort of pattern that may emerge if you were to give them all the same texture map. and there's enough to randomise it so that if you pick a ring and count 8 up the chain it isn't guaranteed to be the same ring
this way you only have to lay out one ring and the rest is essentially copy-paste