According to the Daily Express, Rev Tim Hayes, 52, from St John's church in Dukinfield, Manchester told the Lawrences he would only offer their child a blessing.
Mr Hayes said it was policy at his church is that the parents of a baptised child should be married: "I believe marriage is God's way... [but] it's not so much about what I think; it's about what Jesus thinks."
To emphasise the weight he places on marriage, the vicar said that if money was the problem he would offer couples a wedding ceremony for free.
Heather Lawrence, 30, and partner Jonathan, who have been together for four years, wanted their son Roman christened because they are both Christians and it would "help get the boy a school place".
Ms Lawrence, said: "We can't afford a wedding but we're both Christians.
"When he came around and told us in person, he said: 'Having a christening and having the holy water was not a ticket into heaven'.
"But in my eyes if you are not baptised you can't be bought into the church and you're not one of God's children."
Ms Lawrence said she was also worried the decision could affect Roman's chances of getting into some schools: "There are three schools in our catchment area and two of those require you to be baptised to get into.
"It doesn't matter what religion you are, but they do require you to be baptised."
