(CNN) -- The Coast Guard ended its search Tuesday for two professional football players and a third man lost at sea, leaving the families to cope with unknown fates of the men and to organize a private search.

Loved ones of one of the missing boaters react Tuesday to the news the Coast Guard's search would end. more photos »

"There's a lot of things we have to come to grips with -- we've all agreed unanimously we won't give up hope," said Bruce Cooper, father of Oakland Raiders linebacker Marquis Cooper.

Cooper, NFL free agent Corey Smith and former college football player William Bleakley are missing, with authorities believing a fishing boat carrying them and a fourth man overturned Saturday in the Gulf of Mexico. The Coast Guard search was called off at sundown Tuesday, about 6:30 p.m.

The fourth man, Nick Schuyler, was found alive and sitting atop the overturned boat about 40 miles west of Egmont Key, Florida, on Monday afternoon.

Cooper's father and his friend, Dallas Cowboys defensive tackle Terry "Tank" Johnson, praised the Coast Guard for its efforts, but said they would move forward with plans to organize their own search.

"What we're asking for is experienced aviation pilots" to volunteer for the mission, Johnson said. "We are looking only for experienced pilots ... we don't want another tragedy as we are searching."

Johnson said he had spoken to NFL Commissioner Roger Goodell, and that "we have the support of the entire NFL" in continuing the search.

Neither the league nor Goodell commented on the missing players Tuesday, but Cooper's team, the Oakland Raiders, issued a statement saying the team continues to "closely monitor" the situation.

"We are aware that one of the passengers -- Nick Schuyler -- has been rescued and remain hopeful that the others ... will be located and rescued as well," it said. See photos of Schuyler's rescue »

The team for which Smith most recently played, the Detroit Lions, said: "While we still have that hope, we have begun to cope with the grim reality of this sad and tragic situation."

Earlier Tuesday, Coast Guard Capt. Timothy Close announced the search would conclude in the evening, saying authorities were "extremely confident that if there were any [other] survivors on the surface of the water ... we would have found them." Watch the Coast Guard say it will call off the search »

Bruce Cooper said that when his family received the news that the Coast Guard search was ending, "It got very emotional." He said his son's wife, Rebekah, was trying to rest.

"She is likewise very emotional. She's got a lot of things going through her head, her 3-year-old daughter, for one," he said.

He also said despite his son's career as a pro football player, his first love was deep-sea fishing. "He definitely got lost in his element," Cooper said.

The four friends embarked on a fishing trip in a 21-foot single-engine boat from the Seminole Boat Ramp near Clearwater Pass about 6:30 a.m. Saturday, the Coast Guard said.

Authorities launched a search for them early Sunday after friends and relatives realized the men had not returned.

Close said authorities believe the boat capsized around 5 p.m. Saturday as the men were trying to lift the boat's anchor.

The men were "not wearing life jackets at the time the boat capsized," he said earlier, but "immediately swam under the boat, recovered life jackets and managed to put them on."

The weather was calm when the trip began, but it worsened late Saturday into Sunday, Close said. He said he believed they were aware of the forecast.

Searchers scanned about 24,000 square miles of ocean in about 60 hours, Close said. Authorities found a life jacket and a cooler about 16 miles from where Schuyler and the boat were found Monday, Close said.

Schuyler is suffering from dehydration and hypothermia, making it difficult for him to speak, said his father, Stuart Schuyler. Watch Nick Schuyler's father overjoyed that his son is safe »

Schuyler, who, like Bleakley, used to be a University of South Florida football player, was able to speak to Coast Guard authorities for a short time, Close said. Watch Schuyler being moved on a stretcher »

Schuyler told rescuers that all four men clung to the boat for a time, but then became separated, Close said.

Schuyler last saw his three friends at 2 a.m. Monday, his father told CNN affiliate WTSP-TV on Monday.

Schuyler's mother, Marcia Schuyler, told the Tampa, Florida, television station that thoughts of his family helped to keep him alive.

"He told me: 'Mom, I kept saying you're not going to go to my funeral.' He said that's what kept him hanging on," she said.

Close said he understood there were some plans for amateur searches, and he urged caution.

"We don't want any new search-and-rescue cases resulting from good Samaritan efforts," Close said.

He said Florida Fish and Wildlife Conservation Commission will investigate, in line with state law, and they may attempt to recover the boat sometime Wednesday.

Smith and Cooper were teammates with the Tampa Bay Buccaneers for part of the 2004 season, when Cooper was a rookie, according to the NFL's Web site. Smith, who entered the league with Tampa Bay in 2002, went on to play for the Washington Redskins before moving to the Lions for the 2006 season. Cooper has played for six teams in his five-season career.

Bleakley lettered from 2004 to 2006 as a tight end for USF, and Schuyler was a walk-on defensive end in 2006 but never played in a game, according to a spokesman for the university's athletics department.

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