He has beaten players four years older than him and has even been known to ace his opponents.
Jonah takes lessons four times a week and is being tipped as a future talent to hit British tennis.
Father Jonathan, 45, of Stoney Stanton, near Leicester, said: "I'm told Jonah is some kind of wonder kid, which is pretty amazing.
"He just picked up a racket that was lying around and he started whacking a ball against a wall.
"Most kids his age wouldn't know how to hold a racket, let alone hit it like he does. They just don't have that level of co-ordination.
"Apparently his technical ability is way beyond his years."
Jonah was first spotted at his parent's local David Lloyd Leisure Club in Leicester in May when they took his brother, Hugo, five, and five sisters aged between six and 15 for tennis lessons.
Parents Jonathan, a dentist, and Danielle, both 35, gave Jonah a racket to play with and were stunned by the results.
Mrs Ziff said: "We were totally gobsmacked. The ball came to him and he swung a perfect shot right over the net and past our eldest daughter.
"We thought it must have been a fluke but he did it again and again. He was a natural.
"People were stopping their games and watching in disbelief and Jonah pottered round the court hitting the ball all over the place."
Henry Newball, 36, who coaches Jonah's whole family, praised Jonah's "natural ability".
"At two it's hard to even get a child's concentration for 10 minutes," he said.
"Jonah is obsessed with tennis, which is very unusual for a child his age.
"He started off watching his brother play and wanting to copy him.
"People may see him play and put it down to me but at two it's very difficult to tell them what to do.
Jonah now plays in short 'best of three' games against other youngsters at the club.
He is expected to compete at a junior competition later this year.