The historic, now-vacant Childs Restaurant building on the Coney Island Boardwalk is being eyed for redevelopment as a 5,000-seat concert amphitheater Brooklyn Borough President Marty Markowitz’s signature effort to convert the historic Childs Restaurant into a massive amphitheater is coming down to the wire — and it’s anyone’s guess whether the outgoing captain of Kings will complete his much-desired coup de grace. The City Council is expected to hold a hearing on the complicated proposal to renovate the boardwalk building on Dec. 16. City lawmakers will likely vote on it three days later, when the council holds its last full meeting of the session. “I’m hopeful that the city council will approve it,” said Markowitz. Any delay beyond Jan. 1, however, could doom the project. In September, the Coney Island community board voted against it, arguing that the approximately $35 million in public funds earmarked for the theater and a small park nearby would be better used to help repair infrastructure that was damaged by Superstorm Sandy. And the district’s incoming councilman agrees. “Coney Island cannot become a year-round destination, with jobs and economic opportunity for its residents, without infrastructure and transportation improvements,” said Mark Treyger. Critics have also argued that public money should not be going towards private development of a concert hall. Markowitz defended the plan, noting the building has sat empty for years. “It shouldn’t be held up. There’s no reason to oppose it at that location,” Markowitz said. He’s worked hard to ensure it passes. Markowitz said Monday that he talked to Council Speaker Christine Quinn about the theater plan before he endorsed her last April — a move in which he turned his back on then-Public Advocate Bill de Blasio, who hails from Park Slope. “Any major project that I have championed needs the approval of the city council,” he said. “So would I have spoken to her? You bet!” The unusual $53 million plan calls for the city to buy the Childs building — along with an adjoining lot between W. 21st and W. 22nd Sts. — from iStar Financial, the real estate investment company that acquired the historic structure from a developer after the economy tanked in 2008. According to plans, the amphitheater will seat 5,000 people with room for another 2,000 on a lawn behind it. The performance space could play host to as many as 40 concerts between May and October. Space will also be leased year-round to a yet-to-be-selected proprietor, to operate a restaurant inside the building. This is not the first time Markowitz’s hope of finding a permanent home for his seaside concerts has faced opposition. Public protests in 2009 blocked a planned amphitheater inside Asser Levy Park in Brighton Beach.