I see there's a gap in James's record from 1858-1867, so perhaps his appointment in Shrewsbury was never reported to Cambridge. Those with access to Crockford might be able to tell us more; copies for that period might also include the names of the patrons of the livings concerned.
I've now managed to check the 1874 Crockford myself, and it helps to fill the gaps by showing the following appointments for James:
1850 - Curate of St Mark, Wolverhampton
1853 - Perpetual Curate of Stockingford, Nuneaton
1860 - Curate of Astley, Salop
1861 - Missionary(?) Curate of a district in St Chad, Shrewsbury
(no date given) - Curate of Badby with Newnham, Northants
1867-8 - Rector of Chillenden, Kent
1868-present - Rector of Stowe-Maries, Diocese of Rochester
Looking on at the 1885 edition where both Colings appear, the patron of each parish is given as part of the current incumbent's entry. For Richard, who had been in Chillenden since 1869, the patron is Rev. J. Coling. For James, still in Stowe-Maries, the patron is "present Rector". So it looks as though James owned the patronage of both parishes and nominated himself first to Chillenden and then to Stow-Maries; and nominated Richard to Chillenden as well. This does suggest very strongly that James and Richard were somehow related.
Patronage was (still is?) something that could be bequeathed and inherited, and I believe also bought. Further research would be needed to find out how James came to be patron of these two parishes.