When Marcus Jones and his business partner, Akunna Olumba, set out to open a pizzeria in Detroit, they spoke with banks about their green vision: solar panels on the roof, an energy-efficient tankless water heater and a rooftop system to capture storm water. “The lenders thought we were crazy,” Mr. Jones said. Traditional banks were skeptical that such investments would yield a return, and few had ever issued loans for clean energy or efficiency measures. They told the restaurateurs that it simply was not done. Instead, the pair connected with a so-called green bank, one of a growing number of entities that loan money to businesses and individuals for equipment or technology that reduces the pollution driving climate change....