Have you established any details of Adam's parents, e.g. from his US marriage or death certs ?
Another detail that could be important is the denomination of your McDonald family - e.g. Catholic, Church of Ireland, Presbyterian, Methodist etc.
County Dublin covers quite a few parishes, both Catholic and Church of Ireland, and not all of them have records back to the 1830s. Records from the other denominations are not currently as well represented online. Nearly all of the historic Catholic records in Ireland have been scanned and are available on the National Library of Ireland website, and also indexed on FindMyPast and Ancestry.
Not having a more detailed location, e.g. town or parish, along with no clues to his parents could make this a difficult search, particularly due to the quite early date. Most of the Catholic and Church of Ireland records for Dublin city and some parts of county Dublin are available on the free IrishGenealogy website, I searched these for an Adam McDonald baptism between 1830 and 1840 but didn't spot any good matches, nothing either in the Catholic baptism records.for Co. Dublin parishes as indexed on FMP.
If it were possible to establish details of Adam's parents from US records, then it would be worth searching the Co. Dublin Catholic records again for possible younger siblings of Adam.
edit : noticed that the obit. mentioned a Catholic Cemetery, so presumably the denomination your Adam was baptised into.