You cant. Trying to convince your parents, may only make them mad, if you start bothering them, about getting a tattoo. They may have different thoughts about tattoos, and desecration of the skin... So, while you live under their roof, you have to abide by their rules. When you move out on your own, you can get all the tattoos you want. But for now, I would not say anything, and just keep quiet.
I have 9 tattoos, . .. However, I had to wait until I moved out of my parents home at 18