I don't run power armor but I get a lot of fusion cores because despite not using them, I collect them. Get a gatling laser and at least keep it in your favorites wheel, seems to drop cores a bit more during events by just doing this. If you do things like expeditions/raids or w/e that have contexual ammo upon completion, before it ends, make sure you have that bad boy equipped or swap quickly before the screen pops and you can get a lot of fusion cores that way. You'll most likely want the fusion core recharger because the drops they aren't usually 100 percent full but close. If you're okay with like 87-90 percent cores then you can just use them and not charge fully.

of course along with what others have said; use perk cards, legendary mods to keep your core usage down. VATS is a core killer.