There are lots of different diminutive forms for some family members, such as parents and grandparents, the commonest would be 'mummy/mommy/mum/mom for mother, daddy/dad for father, granny for grandmother and grandad for grandfather, but there are many regional variations. As Su Ki said, there is no generally accepted diminutive for uncle (although I have heard 'Unc' used in one town in the north of England). Aunt is often 'Aunty' but generally if a diminutive is wanted for uncle or aunt it is supplied by a shortened version of the first name. For example, my mother's sister, Patricia, is known by me as 'Aunty Pat' and my nephew and niece call me 'Uncle Bram'

There are diminutive forms for parents ( e.g. 'Daddy') and for grandparents ( e.g. 'Granny'). You could call an aunt 'Aunty', but there is no diminutive form of 'uncle'.