Dd just had hers done for her 8th birthday. She started asking a year ago, and I would quite happily have let her, as all the pearl clutching about pierced ears is beyond me. But Dh said no, and I felt it had to be a joint decision, so that was that.
But after a year of her really, really wanting it done, Dh finally relented. I didn’t force it, or try to persuade him. I just kept repeating to her that I was fine with it but Daddy didn’t want her to. Eventually, when she couldn’t think of single other thing she wanted for her 8th birthday, he caved, because at heart he’s a softy.
He now thinks she looks very sweet with her very subtle, teeny little gold studs (and she hasn’t stopped beaming for the four days since she had it done).
This is a child who is not appearance orientated by the way, before anyone starts; she has short bobbed hair because she can’t be faffed with bobbles and clips, she lives in shorts and despises anything pink and sparkly. I don’t know what appealed to her about earrings particularly, but something did. Only one other kid at her school has had it done (and she’s in a different year).
So I would not hold back about how it is her Dad who is against it, and just let her ask him for his reasons. It might be harder for him to say no to her than it is for him to say no to you. If he’s a bit controlling then he may be getting a kick out of saying no to you.
And if she reaches 11 and he’s still intransigent - sod him, just do it. 16 is ridiculous.