Don't know if this is your Elijah, but am sending the records for your info.
Jane
Staffordshire, England: Parish and Probate Records
Staffordshire: Brierley Hill - Registers of Baptisms and Burials, 1766-1800
1771 Baptized
1771 Baptized
1781
County: Staffordshire
Country: England
13 Apr 1781 Elijah of Hanry & Hanh. Cartwright
Staffordshire: Brierley Hill - Registers of Baptisms and Burials, 1766-1800
Baptisms
Baptisms
1793
County: Staffordshire
Country: England
05 Apr 1795 Eleanor dau of Elijah & Nanny Cartwright
Staffordshire: Tettenhall - Registers of Marriages, 1744-1839
Marriages
Marriages
1777
County: Staffordshire
Country: England
25 Jan 1777 Elijah Cartwright, farmer of this p. and Sarah Parsons of the p.
of Bonnegal, aged 19 with consent of Parents Wit: Nancy Parsons, Francis
Parsons. Lic.
Staffordshire: Wolverhampton - Registers of Marriages, 1735-1776
Marriages 1759-1766
Marriages 1759-1766
1766
County: Staffordshire
Country: England
29 Mar 1766 Elijah Cartwright, bach. of Woodford Grange, Wombourn and Mary
Kaye, wid. L
Staffordshire: Brierley Hill - Registers of Baptisms and Burials, 1766-1800
1771 Baptized
1771 Baptized
1776
County: Staffordshire
Country: England
01 Sep 1776 Elijah of John & Elizh. Cartwright