It is not required to have a certification in anything to give private lesssons. However as it was said before being an athlete does not make a trainer be. It is important to have serious knowledge of medical, mechanical, physiology and teaching experience behind you in a certification.
That be said anyone can teach anything, however to be legally bonded in anyform of insurance policy you will need to be accrediably certified or work under someone who is to protect you and your client.
Hope it helps.