It never appears to have had one, at least not within living or cartographic memory: neither the first nor second edition of the Ordnance Survey six-inch maps, from 1841 and 1896, show any structure within the rectangular enclosure. What the site does contain is an ogham stone, still standing beside one of the tombs. Ogham is an early medieval script in which letters are encoded as a series of notches and strokes cut along the edge of a stone, most commonly used to record personal names and lineage. That this one remains in place at all is somewhat fortunate; a second ogham stone, bearing a Maltese cross within a circle, a spear-like motif, and a swastika symbol flanking it on either side, was removed to the National Museum of Ireland in the mid-nineteenth century.

The ecclesiastical history of the site is a tangle of competing interpretations. A church dedicated to the parish of Minard appears in the Papal Taxation List of 1302 to 1307 for the diocese of Ardfert, and by 1633 it was under the patronage of the Earl of Orrery. Foundations of a church were once visible within the graveyard, though local tradition held that this structure dated only to the mid-seventeenth century and had been relocated from elsewhere, possibly following the destruction of nearby Minard Castle in 1650. One reading of the archaeology suggests that Kilmurry was the original parish church, later moved to Aglish; another, advanced by Hickson in 1888, argues the reverse: that a thirteenth-century parish church stood at Aglish first, and that Kilmurry was only built after 1307, once Aglish had fallen into decay or outgrown its use. Neither version is settled.

The ogham stone that remains on site measures roughly 0.9 metres in height. The scholar R.A.S. Macalister, working in 1945, read its inscription along the northwest angle as CELI AVI VU, with the first two letters uncertain, and noted further ogham scores on the northeast angle that are no longer visible. The stone removed to the National Museum carried an inscription read by Macalister as MAQI MAQ(I....O)GGODIKA, the script running inverted relative to the carved cross above it. The graveyard is accessible off a minor road from the N86, set on a sharply sloping hillside with views south across Dingle Bay, though mature sycamore trees along the southern and eastern edges now obscure much of what was once an open outlook.