If 31 July was recorded as her birthday, the bapt could have been days or weeks later. Possibilities were Mary Lawson bapt 9 Aug.1816 Saint George, Douglas dau of James Lawson & Esther Kneen, Mary Ann Quine bapt 25 Aug 1816 Malew dau of Wm QUINE & Mary Ann BRIGGS, and Mary Ann COWIN bapt 20 Aug.1816 Kirk German dau of James COWIN & Margt KAIGHER, plus a couple of other Marys bapt Malew & German in Nov & Dec. Several bapts after July 1816 also in other parishes, including four in Jurby in Oct & Nov., but the only one found on the exact date you have was Mary Christian in Ramsey - seems too much of a coincidence not to be the right one?

Sue