Officials said a change in the weather might have contributed to the accident.
One survivor, 14-year-old Christopher Duarte, swam ashore to north Tiverton and had a resident call for help about 1 a.m.
"He was obviously shaken up and concerned," Lt. Cmdr. Peter Martin of the Coast Guard told CBS Radio News. "The water was pretty cold."
Duarte's father, 35-year-old Allen Duarte, was later rescued and remained in critical condition in the hospital.
Tiverton police Chief Thomas Blakey said authorities were still searching for the boy's aunt, 24-year-old Kelleigh Ouellette.
The dead included the boy's mother, Edwina Duarte, 34; the boy's cousin, James Duarte, 23; and Ouellette's boyfriend, Richard Doehler, 39. All of the boat's passengers were from Fall River, Mass.
"This is a family excursion that went awry, and it's a tragedy," Blakey told The Associated Press.
Blakey said the group had gone out in the 17-foot pleasure boat during the day, and had traveled to Swansea, Mass., to meet with family. The group left Swansea after dark and was heading to Fall River when the boat capsized, Blakey said.
The time of the accident was not immediately clear.
"The weather had changed. Winds had picked up," Blakey said. "I'm sure weather conditions were a factor. ... "Everything is open. We're looking at weather, equipment, human error. everything."
The National Weather Service said that at 10 p.m., winds in the nearby Newport area were out of the northwest about 9 mph. At midnight, winds were out of the north at 21 mph, with gusts up to 30 mph. Skies were clear and temperatures were in the low 60s to upper 50s.
The Coast Guard said the water temperature was about 50 degrees.
Blakey said the boy was wearing a floatation device, and after the accident, he somehow made it to shore and went to a residence to call for help. Authorities received the call at 1:11 a.m.
Karen Rose of Tiverton had fallen asleep on her sofa but woke up to a frantic knocking and the repeated ringing of her doorbell.
She opened the door to find the 14-year-old boy, shivering and soaked to the bone.
Rose said the boy was wearing a T-shirt, shorts and had no shoes. His feet were cut because he had walked through shells and briars on the beach.
Blakey said police found the boy's father at about 1:30 a.m.
"The quick response probably saved this guy," Blakey said.
Mount Hope Bay is a lobe of Narragansett Bay, with shoreline in Massachusetts and Rhode Island. The bay is north of the Sakonnet River.
Blakey said the boat capsized on the border of the Sakonnet River and Mount Hope Bay, between Fall River and Tiverton.
Coast Guard Capt. Judy Keene said the tide had pulled the boat and the victims to the south. The boy swam to shore about 2 miles north of the Sakonnet River Bridge, while the boat was recovered farther south — about a third of a mile north of the bridge.
The bodies of the victims were found both to the north and south of the bridge.
On Saturday, the Coast Guard was using a helicopter and boats to search for Ouellette. State and local authorities from both Rhode Island and Massachusetts were assisting in the search. Officials in orange jumpsuits used binoculars to scan the shoreline as a patrol boat traveled up and down the Sakonnet River area.
Keene said officials would be evaluating factors such as the air and water temperatures to determine whether the search would be suspended.
Don Dettlinger, an assistant harbor master for Tiverton, said the weather may have created dangerous conditions on Friday night. He also said the boat may have been overcrowded.
"People don't heed weather warnings," Dettlinger said. "It's risky. Why those people were out there last night is beyond my belief. I wouldn't be out if I were on my boat."