I'm finding things in Pinocchio all the time that are not in dictionaries. On p24 of the modern edition:

This must mean "I don't have a single thing I could give you", but pioc-a-mhair is not found anywhere. Would you say it is pioc+maireann?

It looks like it could be interpreted as a verbal noun rendered from the verb mair, other than the expected form maireachtáil, which then came to be embedded in this phrase. Perhaps a dialectal variant? If that's the correct analysis, then I'd interpret the a as Ó Dónaill's a4, "Used to connect a preceding noun or pron. with vn." as in Uisce a ól. So a literal translation of pioc-a-mhair might be "scrap-to-survive [on]".

Because I don't know of any dialectal use of mair in place of maireachtáil, though, I'm inclined to think it may be a fossilised use of the verb with a relative a, where pioc-a-mhair means "a scrap which survives/remains", but the phrase itself can be use nominally "a remaining-scrap to give you".

In any event, I think your intuition about what it means is on the ball, and a reasonable idiomatic translation of what's going on, other than the one you gave above, might be "I don't even have a last-remaining-morsel that I could give you".

Thank you. Maireachtáil is maireachtaint in Muskerry Irish (with the accent on the middle syllable: muh-RAKH-tint).

It does mean "not a bit", although when I've heard it in Kerry it was "pioc a mhaireas":

Ní dhéanfaidh an leigheas san pioc a mhaireas duit.

I always took it as a frozen form of the relative like "iad seo a leanas", meaning "a bit that remains" thus "a bit left".

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

Thank you a lot. I didn't realise it was was more widely found in any form. Yes, that makes sense now.