Just one indexed entry in Bristol parish registers 1538-1812 (Ancestry) for Alexander Don*n and that was for a Donaldson married in 1771.
With no first name found one Daniel Donnovan married in 1701.
Using Alexander D*n*n no results
Using no first name D*n*n lots of Donns, Downings etc but nothing resembling Doniphan even amongst the odd spellings.
Just putting Doniphan into the general search engine with no dates only results in Donivan and Donovan
Simple search Doniphan, Bristol archives no result. Nothing in right period Donovan, no result Donnovan, Donivan, Donnivan
Only Doniphan in national archives is an American ship named Alexander Doniphan in 1945