The baby boy was found inside a Tesco Bag for Life last Wednesday morning on the doorstep of the vicarage to St Peter’s Church on Hough Lane in Bramley,
The crowdfunding appeal at on the JustGiving website has been launched by Haley Hodgson and is aiming to raise £1,500.
Haley Hodgson wrote on the page: “The baby boy many have named Peter was rushed by ambulance to Leeds General infirmary but sadly passed away soon after he was admitted.
“The circumstances surrounding his birth, who gave birth to him, where and how he was born are unknown.
“What we do know to be true and all share is the sadness, grief and loss of this beautiful baby boy who was born in to this world in these horrendous circumstances before he passed away.
“This baby deserves a beautiful named headstone! I’m hoping for people to donate whatever they can so we can give him the best headstone and send off he deserves.”
The Rev Paul Crabb, who found the baby boy outside the church, led prayers for the newborn and his unknown mother at an outdoor ceremony on Friday.
To a gathering of about 50 men, women and children, the vicar said: “We’re here to be together, to share our sadness and to express our love for a little boy we never knew, yet whose death has changed our lives.
“We gather to hold in our hearts his mother, hoping and praying that she will find the help that she needs.”
Floral tributes and teddy bears have been left outside the church in Hough Lane.
After leading three prayers, Rev Crabb asked those gathered to keep the baby boy and his mother in their thoughts.
Some of those who attended spoke of their sadness.
Staff from nearby St Peter’s CE Primary School, who did not wish to be named, said: “It’s all so very sad for a young tiny thing coming into the world that’s gone away so quickly.”
Lisa Longbottom, who lives locally, said: “I hope they find the mum. I really do feel for her at the moment having given birth three times myself I know it is traumatic at the best of times so for her now to be on her own and the state she must be in, it’s heartbreaking.” Police said the baby boy had reached full term and the placenta was attached when he was found. It is believed the bag was left on Tuesday evening or early Wednesday. The appeal page can be found at ww.justgiving.com/crowdfunding/haley-hodgson