Yes.Also, any Eidolon with the Arms evolution can wear rings, which means they can wear a ring of counterspells with the banishment spell stored inside.
LOL, I had this image of the eidolon in question brandishing a ring of banishment in a kind of heroic gesture pose and saying, "I don't think so"!
OK, then the whole banishment thing and sorry if earlier I was sounding a little defensive.
On a separate note does an item that grants SR stack with a natural SR?
It does but the SR stacking rules are REALLY WEIRD so unless you've managed to track them down you would just be guessing at it.
Something like a second source of SR that is under 13 is +1 to existing higher SR, a second source of SR between 13 and 17 is +2....
Something long those lines, a real pain in the neck to deal with lol.
(Note I haven't read these rules in a while I may be off-base)
Page 565 in the core rulebook "Spell resistance does not stack, but rather overlaps."