But by midday the site had crashed after a large-scale denial of service attack.
The IP addresses associated with the attack were being actively blocked and by 2pm the website was up and running again.
However, by 5pm the website domain had been completely removed.
"Due to large scale Denial of Service attacks against this domain it has been decided to ensure the stability and security of our servers and network this account has been removed,'' the web host said.
It was not known where the attacks were coming from, Mr McCoskrie said.
Mr McCoskrie was told it was a fairly major attack, which was aimed at the protectmarriage website but also took down quite a few of the host's other websites.
"You always hope you can have a robust debate about ideas, and show respect for each other but when you're trying to take out each other's website it kind of suggests that you're not going to get a good debate, so that's disappointing."
In explaining the website this morning Mr McCoskrie said politicians had been hammered recently with reasons to redefine marriage, and the website would help to balance the debate.
"Ultimately, the state - which did not invent marriage - has no authority to re-invent it,"he said.
"Equality does not mean we must redefine marriage. Same-sex couples have the option of civil unions to recognise their relationship so there is no need for redefining marriage."
Adding to the website's early-launch woes, US band Train is also vowing to get one of their songs removed from the website, after a YouTube link to the song Marry Me was placed on the website without them knowing.
Train was asked yesterday by a New Zealand tweeter, @Mikey_J_S, why their music video appeared on the website.
Train responded: "Didn't know. Getting it off asap. Tnx 4 tip''.
Mr McCoskrie said he had not yet heard from Train, and the song remained on the website.
"We're not going to do anything based on Twitter, but if they contact us and ask us to remove, we will certainly respect their wishes."
Initial indications are that the bill has the numbers to pass. Of the 76 of Parliament's 122 MPs who responded to a New Zealand Herald survey last week, a clear majority of 43 were in support of the bill or leaning towards backing it.
Labour leader David Shearer has said he will support the bill, and Prime Minister John Key today said he would vote in favour the bill.