Let the J.R. Smith Sweepstakes begin! As NBA free agency begins Sunday night at midnight, the success of the Knicks’ July will hinge on whether they keep their own free agents as much as bringing in new blood, as Smith, point guard Pablo Prigioni and forward Chris Copeland all could fly the coop. Regardless of Prigioni’s situation, the Knicks are bent on adding another point guard because of Jason Kidd’s retirement. The Pistons’ Will Bynum, Brooklyn’s C.J. Watson and and Atlanta’s Devin Harris are on the radar. The Knicks also want to add a backup big because of Amar’e Stoudemire’s uncertain health. Two local products, Elton Brand and Lamar Odom, are targets. The Knicks also will entertain re-signing Kenyon Martin. Problem is, the Knicks have just one $3.19 million mini mid-level exception to spend and the veteran’s minimum of $1.4 million to sign free agents. They conceivably could have to use a portion of the mini-midlevel to retain Prigioni or Copeland. The new collective bargaining agreement has put them in a giant hole, because they no longer can obtain a free agent via sign-and-trade because they are over the luxury-tax threshold. According to a person who spoke to Smith, the explosive but flaky shooting guard believes he will get an offer that will top the Knicks’ maximum bid — starting at $5.4 million — under early-Bird-rights bylaws. The Sixth Man Award winner who flopped in the playoffs then must decide if he wants to take a little less to stay in his hometown and perhaps play alongside his brother, Chris Smith. The Knicks believe odds are they will retain J.R. Smith, but it hardly is a guarantee considering the bevy of under-the-cap clubs and a weak free-agent class. The Bucks, Pistons and Suns are contemplating throwing money Smith’s way. The Knicks are resigned to the notion Copeland will take the money and run. He is coming off a minimum contract of $472,000 and is seeking “Steve Novak money’’ — four years, $16 million. The Pelicans will make a run at Copeland, as reported by The Post. The Pacers also have interest, as do the under-the-cap Mavericks and Bucks.