Well, he never met Morty C-137 before then. Since he helped build the Citadel, he’d probably encountered Mortys in the past.
He may have watched a baby Morty. Or Morty C-137 may have been watched by a different Rick.
He wasn’t specifically looking for a Rickless Beth - he just happened to crash Ship on Earth C-137 while blind drunk and happened to encounter one. As established back in season 1, there’s probably only a single-digit number of Earths within the Central Finite Curve that resemble C-137 (Beth is alive, Morty and Summer exist, Beth is still married to Jerry rather than Paul Fleishman, and Rick has been missing since shortly after Summer was born), so it’s probably the first time he’d stumbled into that set of circumstances where he found a Beth expecting a Rick to come back, and decided to stay.
As to why he never encountered a Rickless Diane - maybe that subset of universes is even more rare than the C-137-types? We’ve certainly never seen another Diane thus far, and it definitely seems to be implied that the Ricks have learned how to artificially produce Mortys to meet demand rather than seek out universes where they developed naturally, so the number of Ricks that actually have a successful family life and a daughter that grows up to have children of her own may be quite small in the cosmic scheme of things.