(covers information from several alternate timelines)
In 2365 during an encounter with the Ferengi, Riker told Picard that "we're all here – anxiously waiting for you to pull another rabbit out of your hat.", referring to a magician's trick. Ezri Dax used the same expression in 2375 on AR-558. That same year, Miles O'Brien twisted the expression, saying to Dr. Bashir, "You're not going to pull a rabbit out of your medkit." He was referring to Bashir's failure to find a cure for the morphogenic virus. (TNG: "Peak Performance"; DS9: "The Siege of AR-558", "Tacking Into the Wind")
In 2372 in Quark's on Deep Space 9, Dr. Bashir pulled a piece of latinum from Quark's ear, a trick taught to him by Jadzia Dax, he told Kira that "next time I want to pull a rabbit out of his ear." (DS9: "Rejoined")
Types of rabbit
"I was hoping you'd be able to pull a rabbit out of that library computer."
"I see no reason why you should expect me to produce a Terran mammal of the leporid family from a machine..."
"A slip of the tongue, Spock."