Henry is listed as William's son:

(1861) Peel Rd, Malew (Dist 6), RG9/4424 f.94 p.14 sch.74
William Quine - head - mar - farmer of 25 acres - b. Arbory
Esther Quine - wife - mar - 53 - farmer's wife - Arbory
Elizabeth Quine - dau - un - 21 - Malew
John Quine - son - un - 19 - Ag Lab - Malew
Thomas Quine - son - 12 - scholr - Malew
Henry Quine - son - 9 - scholar - Malew

(1871) 3 Ballakewin, Malew (Dist 6) RG10/5777 f.153 p.12 sch.60
William Quine - h - m - 66 - farmer of 30 acres - Arbory
Esther Quine - w - m - 63 - farmer's wife - Arbory
Henry Quine - s - u - 19 - farmer's son - Malew

Found them in 1851 too, thanks to Brian's index, as Ancestry has them indexed as 'Quina', :

(1851) Ballakeown, Malew (Dist 6) HO 107/2526 f.102 p.16/17 sch.71
William Quine - h - m - 50 - farmer 30 acres, Malew
Esther Quine - w - m - 42 - Arbory
Margaret Quine - d - u - 15 - Arbory
William Quine - s - u - 13 - scholar - Malew
Elizabeth Quine - d - u - 10 - scholar - Malew
John Quine - s - u - 9 - Malew
Thomas Quine (p.17) - s - u - 2 - Malew

Seven years is a big gap between John & Thomas - perhaps there were 1 or 2 others who didn't survive?

Hope that helps.