Your luck may be in. The company’s records (for all their premises) and their collection of photographs are in PRONI in Belfast. You can search the collection there. The records appear to contain details of who commissioned the photos. Background info here:
Note: "Another interesting and important aspect of the archive is the day-books for the Armagh studio which, apart from two, Sept. 1911-Oct.1915, have survived for posterity. Allison usually inscribed an identification number on his negatives and wrote the number into the day-book. This means that, generally speaking, it takes only a matter of a few minutes to check in the day-book, not only the date of the photograph but also the name of the person who commissioned it. This is obviously an enormous advantage over almost all other photograph collections which have survived in Ireland".