Griffiths Valuation records Robert Grac(e)y in 1863 living in a small house on the farm of Alexander Jameson, in Drumaghadone townland. Modern address is Scolban Rd which is a couple of miles south of Dromore. Should be easy enough to find to day, though whether the Gracey house is still standing is less certain.
Pay no attention to the variation in spelling of the surname. People didn’t bother with exact spellings in Ireland (as Kim has mentioned) and you need to be prepared for many variations when doing Irish research. Usually at the whim of the person recording the information.
Adam’s birth is before the start of statutory birth registration, so you won’t get a birth cert for him. If you want to search for his baptism, then you would need to check the local church records. PRONI in Belfast have the following records for Dromore (which are not on-line):
N.S.P. Dromore Marriages, 1845-95; marriage notice books, 1845-61; stipend books, 1852-1921; session and committee minutes, 1860-1911.
P. 1st Dromore Baptisms, 1832-54 and 1857-1913; marriages, 1845- 1910; committee minutes, 1871-94; membership list, 1835; lists of new communicants, 1836-55.
P. Dromore, Banbridge Road Baptisms, 1851-72; marriages, 1870. Public Record Office of Northern Ireland Crown Copyright 2010 Ref. No. P. Drumlough Baptisms, 1855-1943; marriages, 1871-1936. Marriage notices, 1853-1953.
P = Presbyterian
NSP = Non Subscribing Presbyterian. (Presbyterians who don’t agree with the Westminster Confession of Faith).