MeanMutton, where in the RAW does it say you can't place a spell-like ability into a ring of spell storing? It says that SLA's are very much like spells, and there are at least a couple of ways I know of that allow you to turn your castable spells into Spell-Like Abilities so why not the reverse?
That post was like 4 years ago, and MeanMutton hasn't posted in 3 years. You probably won't get a reply.
Having said that, the answer is that you can't because it doesn't say you can.
A spellcaster can cast any spells into the ring, so long as the total spell levels do not add up to more than 5. ... A spellcaster can use a scroll to put a spell into the minor ring of spell storing.
Just as a character can't fly "just because the rules don't say I can't", a character can't use a SLA in place of a spell here "just because the rules don't say I can't". It does what it says it does and nothing more.
As MeanMutton pointed out (so long ago) the GM can over-rule this. It doesn't seem unreasonable to allow, but it's a house-rule if you do.
(If there's something to contradict me I'm open to changing my mind, but that's how the rules look to me.)