Hello Sonia,
My name is Ken Brown and my Great grandfather and grandmother were Rainbows.
They were from Hanslope and came here to Christchurch, New Zealand in the late 1800's after living, working and raising a family in Bombay, India.
The first generation I can trace is Thomas Rainbow and Ruth Carter who were married in Hanslope on 26th Dec 1822.
If you need information on their subsequent line, I can send you copies of the New Zealand geneology.
Cheers,
Ken