A push on Beacon Hill to bring back happy hour has the support of some Island bar owners who see the potential to attract thirsty patrons in the off-season.

Massachusetts has banned drink specials for nearly 40 years but a bill filed by state Sen. Julian Cyr would allow towns to opt-in on happy hour. The bill, which had a legislative hearing Wednesday, would allow bars and restaurants to sell discounted drinks, though the specials couldn’t extend past 10 p.m. and would need to be advertised at least three days in advance.

Massachusetts is one of the last states in the country that doesn’t allow happy hour and Mr. Cyr. saw the bill as a way to help restaurants and bars bring in more business while also shaking off the state’s sleepy reputation.

“I think Massachusetts has something of a fun problem,” said Mr. Cyr, who represents the Cape and Islands at the state house. “I think it’s something that could help.”

Two prominent bar owners on the Vineyard said they could back the idea, though they likely wouldn’t need it to lure in revelers come summer.

“We don’t have the necessity to discount here on the Island in the high season. We have plenty of demand,” said Larkin Stallings, owner of The Ritz Cafe in Oak Bluffs. “In the off-season, it could be a good tool for giving back to folks who are getting off work and might not have as much money as summer residents.”

Mr. Stallings, who also owns businesses in Texas, said he often uses happy hour discounts in the Lone Star state as a way to draw customers in slow times and it hasn’t caused any problems.

“I’m okay with it,” he said, though he said he didn’t have strong feelings either way.

JB Blau, who owns several bars and Island restaurants, supported giving restaurants the ability to make discounts. He could see happy hour being used to bring in a larger lunch crowd in the shoulder season, or as a way to help businesses attract Islanders in the off-season.

Right now, restaurants can discount drinks, but the specials need to be in place for seven days. That dissuades most businesses from offering drink deals, which in other states are often limited to certain hours of the day or single days of the week.

“It allows a lot of flexibility that right now Massachusetts doesn’t have,” Mr. Blau said.

The ban on happy hour went into place in 1984, after the death of a Weymouth woman who was riding atop a friend’s car in the parking lot of the Ground Round in Braintree. The woman had won several free pitchers of beer at the restaurant.

The death prompted calls for the end of cheap drink deals and has been in place ever since.

Concerns about discounts encouraging over-consumption have been raised in the past, and former Gov. Charlie Baker said he would have likely vetoed the proposal if it came across his desk.

But with Gov. Maura Healey now at the helm, Mr. Cyr saw the potential for the bill to gain a better footing.

Alcohol has been a concern on the Island recently, with Oak Bluffs and Edgartown both banning miniature liquor bottles this year and Oak Bluffs moving up last call. Tisbury only started allowing alcohol to be served without food last year and Chilmark is one of a few remaining dry towns in Massachusetts.

Mr. Blau said he would  want to see “guard rails” on the return of happy hour, such as limits on how low a price can go. Both he and Mr. Larkin said it’s up to restaurant owners to watch patrons’ alcohol intake, no matter what the price of the drink. 

“It shouldn’t cause more over-consumption per person,” Mr. Blau said. “It should bring in more people.”