Can't see a marriage for James Alexander to a Jane Rainey either but wouldn't rule out the Alexander-Leaney one yet.
I did find 3 children listed in IGI:
1. Henry born 17 Mar.1875 Co.Antrim
2. William John born 20 Oct.1876 'Antrim, Ballymoney, Cork, Ireland' (Cork des not belong in the record but LDS have a large batch with Cork in it)
3. Sarah Jane born 6 Feb.1879 Drumaheglis (a townland west of Ballymoney along the River Bann).