The question isn't "can divine smite be stored". It's "can divine smite, which is not a spell at all, but which consumes a spell slot for power, consume a spell that was stored in a ring of spell storing".
I think my answer would be "no" because the ring is not storing a generic-slot, but rather, a specific already-cast spell. But the reason has nothing to do with Divine Smite not being a spell. No one's suggesting that Divine Smite would be stored in the ring.
The point is rather: If I could cast a paladin spell (say, cure wounds) because i have a paladin spell slot, I can use Divine Smite and burn the slot and get +2d8 damage. So if I have a thing that has a stored Cure Wounds, can I use that to get +2d8 damage? I don't think so. But it's not related to whether or not divine smite is a spell.
Yes, this is exactly what I'm trying to ask, thank you.
Th ring says "While wearing this ring, you can cast any spell stored in it." so that is what it lets you do, cast a spell.
Divine smite says "you can expend one spell slot to deal radiant damage to the target." It doesn't say you can convert a spell you cast into a smite.
So the ring doesn't work with smite, it just lets you cast the spell.
This seems right. Fortunately, my DM has allowed me to do it, so... hahahahaha! +2d8 damage an extra five times per day. (When I get two long rests in a row, anyway... which probably won't be often.)
To be fair, storing Wrathful Smite or Thunderous Smite is pretty powerful already.
What spells would you store?