One of my Australian correspondents has kindly sent me a link to an Ireland site that I hadn't come across before. Quite recently the burials at Ballyclug have been listed and can be found at http://genealogygirl.files.wordpress.com/2012/08/ballycluginterments.pdf. There are just two for McIlhagga, both children, as follows:
Samuel, age 5, buried 22 Nov 1896 from Tullygarley, parish of Kells, fee paid 1/";
William, infant, buried 7 Jan 1911 from parish of Ballymena, fee paid 2/6.
I am very uncertain about whose children they were. For Samuel I have a possible birth in the Antrim Registration District for 1891, in their Vol. 1, page 16. I can't get nearer than that. For William, there is a possibility of this being the son of William Hugh McIlhagga and Margaret Boyd, born 9 Jan 1911. However, he was registered William Hugh, though of course the burial record may just say William.