It would be very difficult to know which Irish Distillery it is from unless anything can be glemed from Patersons Archives (if they even exist)
Going by information offered the whiskey would of been bottled in 1964/5.
In 1937 there were a good few actual distilleries still going.
The Royal Irish (Dunvilles) closed in 1938 but it is highly unlikely that someone bought kegs kept them for 27 years then blended them
It Could be any of the big ones of the time. Bushmills, Jamesons, Powers, Old Midleton and Coleraine were all belting out whiskey as single distilleries in 1964 but again it is unlikely that they would sell off expensive old whiskey to be blended.
I reckon it is from 1 of 3 distilleries that closed in the 50's..
Comber closed in 1953 (However it produced pure potstill which would be strange to end up in a blend and actually devalueing the whiskey)
Kilbeggan closed in 1958 but again made pure potstill and was sold off as Kilbeggan but it is not inconcievable that some was sold to independant buyers.
However my best bet would be
Tullamore closed in 1954
This is the only confirmed whiskey that has been sold off after closure to independant bottlers and the whiskey was made to be blended for Tullamore Dew. Eventhough Tullamore continued as a going concern being produced elsewhere the younger stock may have only been held on to as the older stock may not of suited the Tullamore Dew.
This is all just guess work as there is unfortunately very little book-keeping from these distilleries to say where the stock was sold. But any of the 3 above are the most lightly suspects