Hello Elizabeth, at that remove we use church records and over 40% of Church of Ireland records (Anglican or Protestant) were lost in a fire in the civil war of 1921, RC records are patchy at that remove, I did
not locate a baptism but on this subscription site you can search surneame for free and there are only 22 Creen families in Ireland in the 1850s, 16 of these in County Down and 4 in Belfast both now in Northern
Ireland, the two outliers are in Roscommon in the west of Ireland, County Down is close to the Isle of Man but do not try to swim it. https://www.johngrenham.com/ There is also a site for County Down and there
are a lot of Creens there under surnames section. Including some Johns but it is a common name. https://rosdavies.com/SURNAMES/Afrontpage.htm Follow up on the official site for wills and other info on PRONI
see https://www.nidirect.gov.uk/campaigns/public-record-office-northern-ireland-proni
There is a private Facebook group on County Down Genealogy and I see at least one search for a William Creen, it brought back a lot of hits on a search but me thinks I am getting Greens also.
While your man got married in the USA there were 3 Gilliam families in Ireland also.
Good Luck
Pat