Charles and Elizabeth were married in Radcliffe, Bristol, on 22 November 1834.
Have you seen this Redcliffe marriage record yourself? I have only been able to find a submitted entry to the IGI, Charles Dyer and Elizabeth Payne. Is it indexed anywhere else online?
I can't see a record in England of any Charles
Smith Dyer. No reference at all, other than your post and some online trees, which also say that he had a son of the same name, born 1846. But that son appears to have been registered as plain Charles Dyer. And was baptized in Butleigh, 22 March 1846, as Charles Dyer, father Charles Dyer, a saddler (same as on all the Butleigh baptisms, according to FreeReg)
Charles' death was registered in Dec qtr 1894, Wells - Charles Dyer, age 86.
Buried 18 October in Butleigh
No mention anywhere of Smith!