Hi Mary Kay,
The surname Graney is quite rare, with this particular spelling there are only 11 households in the country at the time of Griffiths Valuation.
In the 1910 US census Honora claims she emigrated in 1870 but that is clearly an error either on her behalf or the enumerators.
I did locate a record on Ancestry which might be the one you are looking for.
It records the entry of Honora Garney at New York on 19th Sept 1855 on the ship Margaret Evans.
It's impossible to know for sure but it looks like the right timeframe and the surname could be a spelling mistake.
There are quite a few Edward Fleming records, it is probably not going to be possible to tie him down.
Sorry there is nothing more concrete for you.