The Belfast couple, devout Catholics, never thought of defying the Pope. But the Church's ruling that IVF is sinful struck at the heart of their Catholic upbringing. Having been taught that sex is for marriage and marriage for children, the couple found priests' advice of prayer and acceptance empty.
A few months ago, the Clarkes had IVF treatment at a local hospital. After it failed they transferred to the London Gynaecology and Fertility Centre in Harley Street where their first implant also failed. In a few weeks they will try again. "It was traumatic for us to go against our Church but eventually we squared it with our consciences," said Mrs Clarke. "Connor comes from a family of seven and I come from a family of nine. It was getting that I was the last to hear when a relative became pregnant because everyone knew how upset I would be."
Treatment has proved costly - more than £5,000 so far - and emotionally draining. Their decision to have IVF is still not easy to live with. "I do not want to criticise the Pope," said Mrs Clarke. "It is still all very difficult for us. When I go to London I tell most of my family and friends I am visiting my sister."
The couple limit the number of eggs fertilised so embryos do not have to be frozen for later use or disposed of. They would never allow embryos to be used in research. If large numbers of her eggs were mistakenly fertilised, Mrs Clarke says she would feel morally obliged to implant for as long as it took to use them, no matter the financial and physical cost.
Yesterday she was hopeful that the Pope's comments on IVF - concentrating on the fate of extra embryos - might signal a softening of earlier blanket condemnations.
However, Nicholas Coote, assistant general secretary to Catholic Bishops in England and Wales, said: "The Pope objects to anything that separates procreation from intercourse. When he comments on the extra embryos produced in IVF he is pointing to a worse wrong. It's like saying burglary is wrong but it's worse to go armed." Even a woman who had just one egg removed and fertilised with her husband's sperm would break the Church's teachings.
It was not new for such teachings to be counter to contemporary culture. The Pope recognised human culpability was mitigated by the "structure of sin" in the world.
John Gray, 35, an accountant, and his wife Teresa, 37, a speech therapist, have two daughters conceived through IVF. They believe the church hierarchy is out of touch. "Even providing the sperm in IVF is sinful in the Church's eyes because it involves masturbation," said Mr Gray. "The Pope is living in an ivory tower . . . It's no good praying for a baby when you have damaged Fallopian tubes."
Peter Hegley, director of Issue, the National Fertility Association, said many Catholic IVF couples faced extra moral burdens. But Peter Brinsden, medical director at Bourn Hall Clinic in Cambridge, said most Catholics had reached their own moral accommodation before they arrived for treatment. Most couples followed the normal route; having as many as 15 embryos frozen. Later they were given the choice about whether to implant them in further treatment, destroy them or donate them to research.
Professor Ian Craft, consultant with the London Fertility and Gynaecology Clinic, said the Pope's position on IVF was flawed. A child was the same whether naturally or artificially conceived.
t The names of the infertile couples have been changed.