No, sorry, I've not come across Conningsbys.
I can't see a Coningsby-Whisson marriage on the IGI or on Pallots. Though (while it's not as likely) the Whisson name might have come to the Coningsbys other than by marriage.
The baptism of Robert James Conningsby is on the IGI - 30 Dec 1836 St John The Evangelist, Lambeth Surrey, son of Robert Conningsby and Mary.
Is this them on the 1841 census (HO107/1083, fol. 8, pages 10-11):
Surrey Row(?), Southwark
Robt Coningsby, age 31, cab owner, not born in Surrey
Mary do, age 26, not born in Surrey
Robt Coningsby, age 4, born in Surrey
They're on the 1861 census at 14 New North Street in Finsbury, London (RG9/182, fol. 86, p. 79)
Robert W Coningsby, Head, married, age 52, brass finisher, born in London
Mary A. do., wife, married, age 46, born London
Whisson do, son, unmarried, age 19, brass finisher, born London
Eliza A do, daur, age 16, gold chain maker, born London
Alfred do, son, age 13, office lad, born London
Arthur do, son, age 11, scholar, born London
William C. do, son, age 9, scholar, born London
Frank do, son, age 7, scholar, born London
Mary do, daur, age 5, scholar, born London
Thomas Hayes, visitor, married, age 73, gentleman, born London
I can't immediately spot them on the 1851 census. Whisson Coningsby looks easy to find on the 1781 and 1881 at least.
Presumably you've got Robert Whisson Coningsby's death Q2 1873 Edmonton, 3a, 146?
Pallot's Marriage Index has a marriage of Robert Whisson Coningsby to Mary Anne Lyons, St James Clerkenwell, 1835.