Manchester City Council have five Cemeteries and one Crematorium.

Philips Park Cemetery 1866
Southern Cemetery  1879
Gorton Cemetery 1900
Blackley Cemetery 1953  (Crematorium 1959)
Manchester General Cemetery 1837 (run by M.C.C. in 1938, owned 1958)

Two of these Cemeteries are now closed Manchester General Cemetery and Phillips Park Cemetery,                                (internments still take place to existing grave owners)

Southern Cemetery, Gorton Cemetery and Blackley Cemetery are open cemeteries and the Crematorium situated in  Blackley Cemetery.

Manchester City Council have a burials search website, which is free of charge to search.
If you don't find what your looking for try various spellings as there are quite a few name variations and mis-transcriptions.