The billboard, which said "This Christmas take a moment to think about Christ. Yeah right", sparked complaints it was disgusting and in poor taste.
Mr McCoskrie said the latest billboard showed a lack of Christmas cheer from Tui and would prompt questions from innocent children. The sexual innuendo of the billboard was "adult humour which parents would prefer not to have to explain to children who ask", he said.
"The 'Yeah right' billboards are well known for making people smile. We'd just ask that they do it without embarrassing parents with awkward questions from kids. Keep adult humour to an adult audience - although many adults would be offended by the sign as well.
"We'd encourage families to show their disapproval by boycotting the company products."
Mr McCoskrie appealed to Tui to "show some Christmas cheer and use a family-friendly joke, particularly as there were many families holidaying in the area over the Christmas break".
Family First is considering laying a complaint about the billboard with the Advertising Standards Authority, but does not expect a ruling in its favour.
"By the time they even consider it, the sign will be gone and the damage done. That's why we want a pre-vetting system with community and family representation on the board."
Retired vicar of St Mary's Anglican Parish in Mount Maunganui, Marie Gilpin, said the billboard was inappropriate and at odds with the innocence of Christmas for children.
"It's all bad taste. It has nothing to do with Christmas and the fun and celebration and the innocence of kids' joy.
"The issue is that kids won't realise the connotations that you get from it, but they will ask their parents what they means. The parents are going to have to either answer the question or brush it off."
Mrs Gilpin believed not everyone would "get" the billboard, which she said was a good thing.
Not everyone was offended by the billboard, with the majority of respondents on the Bay of Plenty Times Facebook page finding it funny.
Comments included "Hahahaha that's classic!", "Any TUI billboard is fun.", "HAHAHAHAHAHAHAHA GOLD" and "harmless fun".
But others were not as impressed.
"Try explaining that to the kids, not their best," said Leah Stewart. While Sonya Chapman dismissed it as "not as clever as their usual standard", saying it sounded "like a young teen giggle".
The Bay of Plenty Times Weekend left messages yesterday with the DB Breweries communications manager and Tui brand manager, who did not return calls.
