Jo Meeke and Matt Gurney's son Puck died in hospital following complications in labour.
They have set up an appeal to create an outdoor space for other grieving families and hospital staff.
Ms Meeke, from Bosham in West Sussex, said she hoped the woodland would help people on the "long journey" of coping with the death of a child.
She had an "uncomplicated dream pregnancy" but after complications in labour, Puck was born via emergency Caesarean section on 15 March.
He was transferred from St Richard's Hospital in Chichester to Southampton General Hospital's neonatal ward, where he died the following day.
When it became clear he would not survive, the couple had 30 minutes to say goodbye.
Ms Meeke said the time together had been "a special moment that will live with us forever".
"The hardest thing we're having to deal with now is the immediate raw grief of looking at photos of our son, knowing we're not going to hold that little boy," she said.
"But it's all the other things we had planned for our family moving on - suddenly those things are not going to happen."
The couple has set up the Puck's Promise appeal and aim to crowd-fund £65,000 to buy the woodland.
Mr Gurney said he hoped it would bring "something positive" out of their experience.
"I'd primarily like families who have lost children in some way to be able to use it, for a walk or overnight camp, to be with other people who have been though the same thing."
A couple who lost their newborn baby have raised more than £12,000 towards buying an area of woodland in his name.