First of all thanks to Nadene, Robyn, Rich and Budgie_mad for taking the time to address my issue.
After much angst I decided to add one of my more "friendly" males to the cage and much to my delight they paired up within a few days. Rainbow continued to sit on the eggs and rarely left the box. Gale (a male - named by my son after a character in hunger games) often joined her and cleaned and fed her while she sat on the eggs. However just as with the first clutch and much to my disappointment the second clutch never produced any babies - a few were infertile and the rest were dead in shell. So the lost dad and any potential offspring were lost forever.
However before I removed the 2nd clutch eggs, Rainbow started her third clutch which was unexpected and not intended. Feeling sorry for her and hoping that that the fertility issue may have been linked to the lost dad, I decided to let her continue the clutch with her new partner. I had another couple of budgies with eggs about the same time so figured that they could be back-up if needed. I also took the unusual step of swapping an egg from each clutch about half way through the incubation period as a test.
okay so the first thing that happened much to my delight was that the egg from the other clutch (Wild & Tigers) hatched for Rainbow. The baby appeared weak though, and although Rainbow fed it, it died within a few days. I felt even more sorry for her now but was now starting to think that she must have fertility issue as none of her eggs had hatched.
By this time three eggs in Wild's clutch had started to hatch, including one that hatched and died the same day - so it may not have been Rainow's fault that her baby had died.
But then the big surprise Rainbow's egg hatched in Wild's box and the baby appears healthy - that baby is now nine day's old and thriving with its three genetically unrelated siblings.
Wild's youngest was born last Monday - 6 days later. The amazing thing about this one was we were checking the eggs on Sat afternoon and could hear the baby chirping inside the egg. Something I have never heard. I was a bit concerned on Sunday afternoon when I could no longer hear the chirping and much of the internet forums suggest that a chirping egg should hatch within 12 hours. But Monday morning the little one arrived. So it appears it hatched some 28-40hours after we first heard it chirping.
As for Rainbow she has two eggs left that I suspect are dead in shell. They will be removed and checked in a few days and she will be returned to the aviary for a big rest. It I just a shame that although she will probably meet her own baby, she will never know it is hers.
A friend who I a vet (but not avian ) suggested that Rainow's dead in shell maybe because there is not enough "white" in her shells so that the babies/embryos die of starvation before they a fully developed. I may ever know.