I can only find one baptism for a child of James & Elizabeth and that was for Douglas but as Frances said there are IOM birth registrations that can provide you with dates see this link:-

www.iomfhs.im/resources/births/S.html

Here is the baptism of Douglas:-

Name: Douglas Stuart
Baptism Date: 17 Mar 1880
Event Place: St Thomas, Braddan, Isle of Man
Father's Name: James Stuart, car driver
Mother's Name: Elizabeth Stuart
Abode: Wellington Square
Link: familysearch.org/ark:/61903/1:1:XZ53-1M6