"The boy does his homework."
Translation:Déanann an buachaill a obair bhaile.
A chuid oibre bhaile is certainly better Irish than a obair bhaile for “his homework”.
What do you mean by “likely”? If by “likely” you’d meant “used more often by native speakers”, then you’d need to ask native speakers. If you’d meant “used more often by people with knowledge of Irish, whether native speakers or not”, then you could try using a search engine on each phrase to see which one generates more results.
EDIT: See below — this looks like a case of “nominative in form, genitive in function”, so a chuid obair bhaile would be the preferred form.
I did mean more likely to be used by native speakers (or people with native-like competence). I had done a search for "chuid oibre bhaile" and got only a handful of results: I thought maybe the phrase was too specific to be likely to turn up often in an Internet search but could still be common in speech.
After your reply, I also searched for "chuid obair bhaile", which, though it appears proscriptively incorrect, returned almost 1500 results on Google, including sites such as beo.ie, tuairisc.ie and irishtimes.com. A result from gaelscoilchillmhantain.ie not only has "a chuid obair bhaile" but the result title is "Beartas obair bhaile" and the PDF document linked to is entitled "Polasaí obair bhaile" so "obair bhaile" seems to be getting treated as an invariant adjectival phrase.
Obair in this phrase could be an instance of a noun that’s “nominative in form and genitive in function”. My grammar book shows that when a genitive noun governs a definite genitive noun, the first noun generally keeps the nominative form. (This doesn’t apply to verbal nouns, e.g. lucht foghlamtha na Gaeilge [“learners of Irish”] rather than lucht foghlama na Gaeilge, or to phrases for which the book doesn’t provide a classification.) The possessive phrase a chuid makes obair bhaile definite, so it looks like it’s not one of the exceptional phrases.