Can't help with parents directly, but there may be ways of building up a picture of the HOMER families in the area in the late 18th century, using various sources, as it's not a common name.
First of all, there was a Samuel Homer living at Rowley Regis at the time of the first census in 1841. Born approx 1776, but note that age on this census is approximate (For adults, rounded to nearest 5).
HOMER, Samuel M 65 1776 HOMER, Mary F 60 1781 SHAW, Zaroy M 35 1806 SHAW, Metilda F 35 1806 SHAW, Elezebeth F 8 1833 SHAW, Daniel M 4 1837 SHAW, Samuell M 2 1839 TALBOT, Mary F 75 1766
Piece: 997Book/Folio: 5/52Page: 21 Registration District: Dudley Civil Parish: Rowley Regis Address: Lawrence Lane, Rowley Regis County: Staffordshire
Note: - No relationships were stated on this censnsus. - All above were born in Staffodshire. - On the original image, occupation is given, though very faint. I think Samuel's says 'Ind', meaning 'of independent means', and I think 'Zaroy' (also hard to read) was a nailmaker.