Adisyn-Hope Davidson was stillborn in July last year. Her mother, Emmerson Morgan, was six months' pregnant.
Miss Morgan and her partner Ben Davidson (both 36) wanted more time with their daughter but the hospital in Wellington did not have a ''cuddle cot'' available.
A cuddle cot is a cooling system which is placed into a moses basket and allows parents to have extra days with their dead babies.
Miss Morgan said the cots would help reduce some of the trauma during the ''horrific'' time when parents were ''raw and hurting''.
Mr Davidson said the alternatives were ice packs, which needed to be changed often, or embalming, but often babies were too small to embalm.
The couple brought their daughter home from the hospital in a basket on ice packs, allowing a night together before her funeral the next day.
A cuddle cot gave families more time to ''create memories'' by doing activities such as taking photos or getting plaster casts of the baby's hands and feet.
Miss Morgan said cuddle cots were more common in other countries and some families had up to nine days with their baby.
Some people questioned how a parent could love somebody they never knew, Miss Morgan said.
''The moment I saw that pregnancy test I was in love with her,'' she said.
A cuddle cot cost about $3500 and the couple hoped to raise enough to buy cots for Dunedin Hospital and Wellington Hospital.
• Money could be given at: http://givealittle.co.nz/cause/time4cuddles#
