William does appear with his siblings in the 1851 census living in Adlingfleet where all the other children were also born ( Simpson , Sarah ,Mary Ann, Smith and Thomas were born.)Either he wasn't registered or there is a miss transcription. He doesnt appear on the free bmd index either
There is a family living in Swinefleet Yorkshire, in 1851. William Coult, 24 wife Mary, 31, children William 8, Samuel 6 and Mark. The birthplace of Mary is given as Rawcliffe, Yorkshire.
COULT, SAMUEL PLAXTON
GRO Reference: 1846 S Quarter in GOOLE UNION Volume 23 Page 267
COULT, MARK PLAXTON
GRO Reference: 1849 J Quarter in GOOLE UNION Volume 23 Page 295