I farmed for clay for the Beach farm for Deluxe Retaining Soil, and scoured both my options in game and the internet fairly well for Clay sources. I found the following options offered decent rates of clay accumulation:
- The Dig Site on the Island. Limited by spawn rate, but material dense and easy to intermittently check and farm. I use this constantly.
- Farming large swaths of land (I stopped growing trees in the desert at one point to test on there) using the good old "as large of an area as I can hit and going blind" method. It's not a decent rate, and I couldn't do it. We're talking like trading a day for 30-40, sometimes less.
- Using a predictor and meticulously hoeing successful spot after successful spot. The spawns for hoeing change with each tile tilled. As such you need to hoe, pause, increment the tilled tile counter, see what the new spot is, move there, hoe (hopefully not accidentally off a spot as I would occasionally be), pause, etc. I found it incredibly boring and unfun, and though I tried it once to see what kind of rate of accumulation I could do, the answer was still 'not enough fast enough for me to think it worthwhile'.
- Geode cracking. If like me you have a bunch of extra geodes just laying around, it is worth cracking them open, you can get a decent amount of clay from them (depending on starting quantity). Kinda situational, I used up a year's worth of accumulated geodes in a day, but I did get over 100 clay as a result.
None of those offered me the limitless large scale efficient clay farm I wanted, so I had to pivot my plans, but those are the things I tested. It's my opinion that it's reasonable to expect with frequent trips to the dig site and assuming you mine anything like I do that you can get 1,000 - 1,200 clay per year, but more than that is not realistic without significant effort offering low return value.