Does finneon evolve with a oval stone?

No, it evolves by leveling up, to level 37 I think. sorry to dissapoint you but it can't be evolved with any stone it has to evolve on its own . it evolves at level 31 . i would choose the day care . ps. once in the day care use your bike to ride from route 210 to 209 hope this helped you get the pokeradar and get the national dex and to get these stuff talk to rowan for the poke radar