According to the post cited above, "mo páiste veg asthore" means, literally, "little child, my treasure."

However, the lyrics given in that posting differ slightly from what I see in my facsimile edition of "Songs Sung and Unsung." In that edition, in the original typeset, the lyrics are set forth by Boulton as:
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October winds lament around the Castle of Dromore,
But peace is in her lofty halls, mo páiste veg asthore;
Though autumn leaves may droop and die, a bud of spring are you,
Sing hushabye lullaloo lo lan, sing hushaby lullaloo.

Bring no ill-winds to hinder us, my helpless babe and me,
Dread spirits of the Blackwater, Clan Eoghan's wild banshee;
For Holy Mary, pitying us, in heaven for grace doth sue;
Sing hushabye lullaloo lo lan, sing hushaby lullaloo.

Take time to thrive, my rose of hope, in the garden of Dromore;
Take heed, young eaglet, till your wings have feathers fit to soar.
A little rest, and then the world is full of work to do;
Sing hushabye lullaloo lo lan, sing hushaby lullaloo.
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