He later told the Rotorua Daily Post that Smith was the biological father of the baby and their surrogate mother was "a friend of a friend".
At the time he said the pair hoped to raise more than one child if they "work out how to do it the first time".
🌈👶🏻 He’s here. and he came into this world surrounded by his village. #modernfamilies 👬Mum doing awesome. Dads...
Posted by Tamati Coffey - Labour MP for Waiariki on Tuesday, 9 July 2019
Coffey also tweeted the news.
Coffey was an award-winning presenter who left full-time television in 2013 to pursue a career in politics.
In 2014 he was named the Labour Party candidate for the Rotorua electorate at the general election but missed out to National's Todd McClay.
He stood again for the party in the 2017 election and won the Waiariki Māori electorate, defeating incumbent Māori Party co-leader Te Ururoa Flavell by 1321 votes.
Smith and Coffey announced their engagement in February 2011 and wed in a civil union in December that year.
The pair owns two Rotorua bars together, Ponsonby Rd Lounge Bar and the more recently opened Our House.
They have owned Ponsonby Rd since March 2015 and opened Our House at the end of 2018.