Hi Stacey
Did you purchase the birth cert of Timothy Mcgreal to confirm his parents names.I see a family in 1911 census indexes Liverpool. There is also a Timothy and a Rose who are in an institution. The children of the family of John Mcgreal and Mary Coughlan are listed on the online births but these records only go up to 1906,so Timothy would not be shown.
The Irish Mayo Ancestors site shows a John Mcgreal born 1857 to a James Mcgreal and a Bridget O'Brien.It would not be worth purchasing the record as it only shows the date,denomination and Parish no Townland Address.There is a James Mcgreal in the Griffths Valuation living in Farburren Westport,but this list only shows people renting or owning land so if your ancestor was not a farmer there will be no record.Mostly ignore dates on census records they are often out by 5 -10yrs espically Irish .