Hello Johngirl,
Galway's a county so you probably mean you don't know the townland or parish. If you know Mary's denomination that could assist in the search.
You'll have to rely on Church records as Mary was born prior to the introduction of Civil Registration in Ireland. This happened in 1864. The marriages of Non Catholic were registered from 1845 onwards.
When Griffiths Valuation took place in Galway in 1855 there were families with the surname Allen in the following Parishes ... Annaghdown, Ballymacward, Claregalway, Clonrush, Duniry, Inishcaltra, Kilconnell, Kilcummin, Killeenen, Killosolan, Kiltartan, Lickmolassy, Rahoon, St. Nicholas, Tuam
Christopher