Hi Liz
The children of William Duke & Jane Cain are in the IGI: -
John Juke, baptd 6th Aug 1843 Santon, parents Wm & Jane Cain
James Juke baptd 10th Jan 1847 Santon, parents Wm & Jane Cain
Eliza Jane Deeke!!! baptd 13th Jul 1851 Braddan, parents Wm & Jane Cain
The 1st two I guessed from Brian Lawson's site, which gives the alternative spelling of Juke for Duke; Eliza's name popped up by putting "eliza" into the IGI (not "all records") and giving both parents' names and IoM for birth place, then searched single years around 1852 -out popped Eiza Jane Deeke!.
Also there is a death of a William Duke on Brian's site - Wm Duke, 64yrs buried Braddan 13th Aug 1878. This would fit with Wm Duke b. Arbory in 1813.
The only other thing I can suggest (you may have done this already) is going through Braddan Baptisms for 1860-63 at the Museum Lib looking for any John (Henry) - I found that one of my ancestors (who was a Quine) was born as Gawne. - so you could make a list of all the Johns in those years in Braddan and see if anything fits.
Good Luck
JohnL