Very little is known of Cairnryan. Apparently, two silhouettes, dated 1839, were signed by a Cairnryan. There is no evidence of his or her identity, or whether they produced any more. These two silhouettes are painted simply in black, with white relief.
Source: McKechnie (Author of, British Silhouette Artists and their Work 1760-1860)
Cairnyan (McKechnie Section 2)