People usually farm Depth 5 RFC Chalices that have the Merciless Watchers as the first boss, since they can drop them and aren't terribly hard:
pwmf22gu (Radial)
5pwujscd (Triangle)
As far as I know, there are no equivalent Waning/Circular gems, so you either need to use lesser ones or hunt for Abyssals. (Much, much harder.)
Generally, you just want to run straight to the second part of the 1st layer, rush the gate lever, head straight to the boss, then reset the dungeon (remove the Chalice and re-search it) and do it all again. You're going to get a lot of gems that are rubbish along the way (-ATK, HP Continues to Deplete, etc.), so if you want a full set of 27.2% ones be ready for some grinding. (That said, it's lucrative in terms of Souls; you should net a couple hundred thousand per gem.)
Edit: Oh, and if it isn't clear: this is why people generally prefer to have 2 Radial and 1 Triangle slot on physical weapons. Thankfully, a lot of the DLC weapons come already with these slots.