My husband is descended from Rainbows that lived in Coventry during th 1800's.
His grandfather was Frederick John Griffin Rainbow b 26.7.1841 who married Catherine Bracken on 16 Aug 1864 at St Michael, Coventry.
Frederick's father was John Rainbow bapt 13 Oct 1799 at Burton Dassett who married Bathsheba Griffin (b <1801> at Gaydon). They moved to Coventry where he was an innkeeper at the Dolphin in Cross Cheaping.
John's father was William Rainbowe bapt 29 Jan 1769 at Burton Dassett and who married Elizabeth Coleman 24 Sept 1798 at Shotteswell.
The following fits but isn't proven
William's father was also William Rainbow bapt 26 Jun 1732
at Charlecote and who married Elizabeth Pelvy on 11 Nov 1767
at Burton Dassett.
William's father was John Rainbow born <1705> in Charlecote and and who married Sarah Lewis 28th June 1730 at Charlecote
That's as far back as I have been able to go, do they tie in with any of your Rainbows?