The section on attunement is quite long, so I won't reproduce it here, but it refers exclusively to a "creature". It doesn't say anything about a player, a player character, a humanoid, or anything else that would exclude familiars from being able to attune to magic items.
The ring of spell storing itself likewise has no restriction beyond requiring attunement, so yes, a familiar can attune to it. I feel compelled to point out that some DMs might not allow a pseudodragon to use a ring because it doesn't have fingers, though.
As for concentration, the DMG says this about items that cast spells (on page 141):
The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.
So if you cast a spell into the ring that requires concentration, when your familiar uses the ring to cast it, your familiar will have to maintain concentration, not you.