The woman has been described as having "a very strong faith" by the Assistant Curate at her church.
36-year-old Leigh-Anne Varley told her husband, Simon, 39, and their two children that she was suffering from swelling caused by ovarian cysts.
But the court heard that she had become pregnant as the result of an affair.
James Leigh, Assistant Curate at St Mary's CoE Church, offered the Varley family support after details of the case emerged, according to The Mirror.
He said: "They are regular worshippers. I knew about the baby being found from the press coverage, then found about the court case."
"They are a very stable family, and have a lot of love and support from their relatives and the church.
"It is such a hard situation, we want to support her, but it is hard to know how much support to give.
"She has a very strong faith, all four come to church, they are there every week and are regular worshippers in the congregation.
"Simon had a lot of different things to consider but I do admire he has decided to stick by his wedding vows. I spoke to him about it and he thought that was best for the children.
"They went to Orlando in the summer, it was a dream holiday, something has just gone wrong, these things happen sometimes.
"When I heard I felt so sorry for her. I knew it had been put on the doorstep but did not know she had anything to do with it. It is a very difficult situation."
He added: "They have been to church since the baby was abandoned. They are just a normal family just trying to move on with their lives."
Simon tweeted that "he would not break" earlier in the month.
I will not break, plenty of fight in me, Lucy and Luke are my everything x.
— SIMON (@VARLEY69) September 5, 2015However, speaking to The Mirror, a family member said: "He did not know the full details of what had happened until it all came out in court. I am not sure if he will still be here [at the family home] tomorrow."
The court heard that Mrs Varley planned to give birth at home and after going into labour cut the umbilical cord with kitchen scissors and wrapped the placenta in a carrier bag.
Peterlee magistrates heard that she had put her son to bed, her daughter was out and her husband was on night shift.
She left the baby on a flat doorstep near the local medical centre in Horden, Country Durham.
The baby boy was left wrapped in a dressing gown with a note that read: "Please take care of my baby boy. Please don't go public as my husband is violent and will kill me."
The child was discovered four to five hours afterwards by a man walking his dog.
The boy was left around midnight on 26th May and after leaving the child Mrs Varley went and booked a holiday for her family to Florida.
She left for work as normal the next morning.
In court, accompanied by her family, she admitted abandoning a child contrary to the Children and Young Persons Act 1933.
The court was told that Mr Varley would "stick by marriage vows" after asking for advice from his local church.
The couple had been married 15 years and the court heard that she was still "part of the family unit."
She had confessed to police within hours of the baby being found, but is has been reported that she did not tell her family the full story until the court case.
Sarah Traynor, prosecuting, said: "She admitted the offence and gave a full explanation of the background to the officers.
"She said she had an affair and she believed the baby was the result of that affair.
"She was living at home with her husband and her two children aged six and 16 at the time. She was unable to tell her husband because she was fearful of breaking up the family unit."
She went on to say: "She was unable to have a termination due to the stage of her pregnancy when it was discovered and also the fact that she suffers from epilepsy.
"She researched how to have a home birth and she did so later that day."
The prosecutor added that the next morning: "She saw an ambulance at the scene and the police had taped off the area so she was comforted the baby had been found and was receiving appropriate care.
"She told the police she had concealed the pregnancy by saying she was suffering ovarian cysts and had thrown the positive pregnancy test down the toilet.
"She said she knew what she had done was wrong and she didn't want to keep the baby.
"This is a very sad case, she is of previous good character and was in a desperate situation which led to the offence occurring.
Sheila Ramshaw, mitigating, said: "This poor lady has suffered a lot over several months, she is of impeccable character, she is someone we will never see before the courts again.
"She is part of a family unit and cares very much for her family, to separate them with a custodial sentence would do no one any good.
"The pressure she has been under has led to some mental health issues for which she is now getting care."
Magistrates gave her a 14-week prison sentence suspended for 12 months and ordered her to pay £325 costs.
She was told that if she committed another offence within the year, she'd be sent to prison.
She left the court and made no comment.
The baby boy, found near the Shinwell Medical Centre, was taken to the University of North Tees Hospital in Stockton, where nurses named him Jack.
He has been taken into local authority care.
