HONOLULU—When Ryan Henline’s friends from Maryland came to Hawaii for their honeymoon in April, he rolled out grand plans for them to island hop on his private plane that he flies himself.

They planned to go to Kauai on his Cessna 182, then drive around the island. But no rental cars were available. A car-sharing app was also completely booked.

“We almost didn’t go. Literally on the day of the trip, I wasn’t sure if I’d have a car,” said Mr. Henline, who is a resident on Oahu, a 40-minute flight away. “We’re island-hopping, it is a big adventure, and I have the plane but we just don’t have the car.”

The car rental shortage is tough all over, but it’s especially troublesome in paradise, where much of the appeal for visitors is venturing across the islands at their own pace. Tourists have gotten creative. Some have made personal appeals over social media. Some are renting from locals who have spotted the demand from tourists and are offering their own cars for a fee. A few have rented the only ride at a price they could find palatable: moving vans.

Mr. Henline, 42, said he had contacted someone who listed a personal vehicle for rent on Craigslist, but appeared to have a change of heart. “He didn’t seem like he wanted to rent the car. It took a bit of conversation,” he said, adding that they bonded over a skill they possess: both were helicopter pilots. He got the car: a Dodge Grand Caravan that cost $225 a day.

Last year, rental-car companies sold part of their fleets and shipped many vehicles in Hawaii to the mainland to accommodate pandemic-weary Americans who hit the roads. The islands had strict entry requirements and tourism plummeted by as much as 99% during the early months of the pandemic.

This year, as vaccinations progressed, Hawaii gradually loosened its restrictions to domestic travelers, and travel rebounded faster than many businesses had anticipated

The Hawaii Tourism Authority said the state’s rental-car fleet decreased by more than 40% during the pandemic and currently advises tourists to secure a car reservation before making other travel arrangements. Preliminary estimates show visitor arrivals reached 630,000 in May, compared with roughly 9,100 from the same period in 2020.

In May, some visitors complained companies had overbooked them. “They’re telling us that there are no more cars and they have overbooked everybody,” said Paula Tarleton, in email while waiting in the Avis line at Kauai airport. Avis took many of them back to their hotels in the shuttle.

Avis said it had been challenging to predict consumer demand in Kauai in the early days after travel restrictions were reduced.

Ms. Tarleton’s luck turned around the next morning when she called Avis at 6:30, and someone answered the phone saying there was a 6-person van for her—perfect for her and her five-person travel crew.

Travelers are swapping tips on how to have a more pleasant experience. If there is a longer wait at the car-rental counter, come with a great attitude, a full battery charge on the phone and make friends with the people in line, a Reddit post said.

Car-rental companies said they have moved hundreds of cars to Hawaii in recent weeks, and that the squeeze is less acute. They encourage customers to make reservations in advance.

An aerial view of Honolulu. Tourism is up in Hawaii.

An aerial view of Honolulu. Tourism is up in Hawaii.

Photo: Kent Nishimura/Los Angeles Times/Getty Images

“Kauai is the Hawaiian island to have travel restrictions reduced most recently, making it challenging to predict consumer demand patterns and airline capacity,” said an Avis Budget Group representative, adding that the company will continue to adjust its fleet to accommodate changes in the market. The company said it transported hundreds of vehicles to Hawaii in late May, and vehicle shortages have been addressed.

A spokesman for Turo, an app where individuals can list their own vehicles for rent, said “we are hearing from our hosts in Hawaii that they cannot add cars fast enough to keep up with the demand.”

Some have resorted to booking moving vans. The Hawaii Tourism Authority says on its website that it “doesn’t condone visitors renting moving trucks and vans for leisure purposes.” A spokeswoman said this is still happening and the reminder remains necessary.

Clayton Robbertze, chief executive at the Rent-A-Wreck Kauai car-rental business, said he had to upgrade the phone systems recently to accommodate the huge increase in inquiries, from around 40 emails and calls a day to 500 to 1,000.

“They come and they’re crying on the phone,” said Mr. Robbertze, referring to customers who said they have been stranded after their car reservations were canceled by others at the last moment. He added that some customers are sharing cars or accepting that they may only have a vehicle for a few days rather than for their entire trip.

Christine Deng and her boyfriend Michael Keller in Oahu.

Christine Deng and her boyfriend Michael Keller in Oahu.

Photo: Michael Keller

Christine Deng, a Bay Area resident who recently spent a month in Oahu, said she had to be creative. “By the time I checked, the only options were Teslas and Maseratis,” said Ms. Deng, a designer. She said prices rose from $60 a day to $400 a day, and desperate, she started asking everyone she knew on the island and friends from the mainland if they had anyone to recommend renting a car from.

Ms. Deng and her boyfriend decided to take the bus, bike or walk to destinations for most of their trip. “I got him really tired from the walking,” she said.

She also studied prices on car-sharing and ride-sharing apps and found that waking up one morning at 5:30 got a cheaper ride to a popular hiking trail. “It was $35, and it could easily be $80 if I booked it later,” she said.

Kaci Barker, with her husband in Hawaii, found a car for rent through Facebook.

Kaci Barker, with her husband in Hawaii, found a car for rent through Facebook.

Photo: Kaci Barker

Kaci Barker, a resident of Austin, planned her June honeymoon trip to Kauai in April but later found out rental cars were booked. The 29-year-old tried to talk herself into accepting being confined in a resort.

“I guess we won’t be doing anything on our overpriced trip,” Ms. Barker said in early June, around a week before her trip. Days later, through Facebook, she found a local car owner willing to rent her a 2017 Honda Accord Sport, Ms. Barker said. The cost: $200 a day.

This summer it’s harder than ever to rent a car in the U.S., especially at popular vacation destinations. To learn what’s behind the spike in rental car prices, WSJ speaks with an industry analyst and WSJ’s Nora Naughton. Photo: Luke Sharrett/Bloomberg The Wall Street Journal Interactive Edition

Other travelers said they have been able to make do without a car. In May, Eric Rubens stayed at the Four Seasons Resort Oahu at Ko Olina with his wife and 2-month-old daughter for five days. It was his fifth trip to Oahu, and the first one without a car.

“It was already going to be a compromised trip,” said Mr. Rubens, referring to the limits of traveling with a newborn. “Having a baby is a full-time job, there are fewer hours in the day to do stuff. If it is just me and my wife, we’d be sitting around looking for things to do.”

There was a brief inconvenience halfway through.

“We kinda got into trouble, we didn’t have enough diapers,” said Mr. Rubens, an outdoor photographer. “Thankfully Target offered same-day delivery.”

Write to Esther Fung at esther.fung@wsj.com