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."

He is wounded and dying, writing a moving final letter to his loved ones.
But he is not fighting and he is not in a war.
Piaras is, in fact, only 11 years old, and he is portraying the last hours of Michael Joseph O'Rahilly, killed while taking part in the 1916 Easter Rising.
The drama "The Death of The O'Rahilly" is just one of the ways Holy Cross Boys Primary School in Ardoyne in north Belfast is marking the centenary.
The school has devised a special 1916-2016 education programme, placing the rising at the centre of their curriculum.
They have been teaching special lessons in geography, music, art and English.
But it was O'Rahilly's story, and letter, which captivated Piaras.
"It is a myth that he wrote it in his own blood," he said.
"But by the time the letter was delivered, he was already dead."
The school's short drama now has a chance of being performed on the stage of the Abbey Theatre in Dublin.
They have been shortlisted as one of only six schools across Ireland in a competition run by the famous theatre.
Meanwhile, in another classroom, P4 to P7 boys who are members of the school council are updating the 1916 proclamation.
Their 'Proclamation for a New Generation' takes the form of Padraig Pearse's famous document, but updates it for the 21st century.
It contains hopes for "a good job and good health care" and a commitment that "Ireland will be litter free".
"It does not matter what gender you are, what colour your skin is, what religion you believe in," it reads.
"All children of the nation will be cherished equally.
"Our Irish traditions, language and sport will be passed on to our children and grandchildren."
The proclamation will be revealed to the whole school at a special assembly in mid-March.
Elsewhere, pupils have been learning the names and locations of Ireland's 32 counties in geography, while others have been composing a song on the theme of 1916.
But is there a danger the focus on the rising could lead to indoctrination rather than education?
It is concern answered by the school's vice-principal Chris Donnelly, who said they take a rounded approach to history.
"What we're about is teaching across the length and breadth of historical issues," he said.
"In this school we teach the world wars, and the boys in primary four go to the Northern Ireland war museum every year.
"The principal has taken boys to meet Queen Elizabeth when she came here.
"The Easter Rising was a significant event in Irish history and therefore it does need to be talked about and taught.
"The boys will be aware from the community and what they see around them that it's the 100th anniversary.
"We're using that theme in a forward looking sense with the proclamation for a new generation."
A couple who lost their newborn baby have raised more than £12,000 towards buying an area of woodland in his name.
[NEXT_CONCEPT]
Piaras Millar sits before me, bloodied and bruised, in the green uniform of a soldier.