In Bridge Field in the Wild Area, there is a second daycare. On the right hand wall, if you follow it down, there will be two NPCs. They are the digging duo. The left one focuses on skill, and the right on stamina. By talking to one, you can spend 500 watts and they'll start digging. There is a small chance that they'll find a fossil. I have about 7 of each, except I have no Fossilized Birds. That's just bad luck for me, though. Credit to VelvetBanshee and Potface64 for answering before, but I thought I'd go into more detail. Thanks!