Larkspur has already given a list of possible baptisms for Elizabeth Wright in Notts, I've extended it by looking at all churches and chapels in the town, 1765-75; this gives a total of 8.
1767 02 03 Elisabeth John WRIGHT Kezia NOTTINGHAM St Mary (one other child, William)
1768 06 23 Dau Elizabeth Thomas WRIGHT Mary NOTTINGHAM Castle Gate, Independent (already ruled out)
1768 11 21 Elisabeth William WRIGHT Martha NOTTINGHAM St Mary (several other baptisms but with names that aren't reused eg Lydia, Anthony, Lucy)
1770 08 18 Elizabeth John WRIGHT Jane NOTTINGHAM St Mary (buried 22 Aug 1770)
1770 09 09 Elizabeth Edward WRIGHT Eliz'th NOTTINGHAM St Peter (Edward was a butcher. Oldest child, Mary, bapt at independent chapel; 3 more children at St Peter - Nathaniel, Elizabeth, Edward)
1772 08 03 Elizabeth Charles WRIGHT Elizabeth NOTTINGHAM St Mary (again, many less common names in this family - Robert, Charlotte, Cornelius, Molly)
1772 08 21 Dau Elizabeth Thoms. WRIGHT Mary NOTTINGHAM Castle Gate, Independent (already ruled out)
1774 01 27 Elizabeth Anthony WRIGHT Elizabeth NOTTINGHAM St Mary (The oldest of 5 children to this couple; Elizabeth,Mary, Anthony, Ann, Mary)
1774 11 22 Elizabeth Thomas WRIGHT Susanna NOTTINGHAM St Mary (9 baptisms in total, all commonly used names)
1775 03 20 Elizabeth William WRIGHT Elizabeth NOTTINGHAM St Mary (8 baptisms - Henry, Mary, Elizabeth x2, James, William, John x2)
jonwarrn has posted whilst I was typing; if 1770 is correct then Edward and Elizabeth look like the parents. Any wills available for Edward?