Hi Matt
Never heard of The Kings Church, even less so an Anglican church that also had the ability to carry out burials in the area. I have a bit of knowledge of this area as one of my ancestors is buried there and have studied all the chapels and churches around and about Arnold.
I can only suggest they are buried at St Mary's Church, Church Lane, Arnold which was where all burials were carried out up until the churchyard was full. I have details of burials from 1672 to 1901 let us know what the surnames of your ancestors are and I will look them up see if they are there.
The other Arnold Churches/Chapels were: Salvation Army, Congregational, Wesleyan, Front Street Baptist, Primitive Methodist, Red Hill Baptist, Gospel Mission, Daybrook Baptist, Ebenezer Chapel and Cross Street Baptist.
There are many families buried at St Marys Church. The families of Redgate, Sturtevant, Settles, Need, Oscroft, Frost, Morris, Moore, Rhodes, Newham, Stanfield, Surgey, Dickinson, Simkin, Clay, Williamson, Blatherwick, Bryan, Phipps, Leverton, Alvey, Atherley, Lee, Gill, Truman, Askew, Hearson, Dove, Smedley, Wilkinson, Dean, Skerritt, Barrow, Jones, Challand, Shelton, Allcock, Jeffrey, Bacon, Bradbury, Ward, Holbrook, Pembleton, Jackson, Gadsby, Parr, Howitt, Kelk, Burton, Bradley, Mellors, Marshall, Wood, Garratt, Lamin, Stones, Hart, Clarke, Chadburn, Simpson, Holt, Jew, Worton, Extall, Showell, George, Kendall, Stretch, Robinson, Acton, Mann, Godfrey, Prior, Hartshorn, Peck, and Willows are among the many families whose ancestors are represented in the inscriptions.
Acton. The burying-ground of the Acton family, ancestors and relatives of Mr. James Acton, of Goodwood House, is a carefully kept plot just inside the gate of the north Churchyard. Thomas Sheldon, died 1875, aged 80; he fought at Waterloo. (Thomas was my Great, Great, Great, Great Uncle)
One interesting fact about when the Churchyard was enlarged in about 1851. At the Consecration a young man named John Toplis was present, and when the ceremony was over he exclaimed, "I wonder what poor devil will be buried there first." Soon after reaching home he was seized with small-pox, and died in three days, his own interment thus giving a very prompt and unexpected reply to the question.
Regards
Mike