SLANE (the same as Roger's link) is a tune name used in hymnals. Hymns Ancient and Modern (New Standard) (1983) says it is "Irish traditional melody." To this, "Be Thou My Vision" (tr. by Mary Byrne; versified by Eleanor H.Hull) is usually set. For its words and MIDI, click here.

Whether Thomas Moore wrote a poem to this tune or not, I do not know. I have a copy of Irish Melodies, new edition (Longmans, Green, and Comapny, 1873), but cannot find it either. Moore's Irish Melodies sites are here and here.