I know I am going to get a mouthful for saying this but go and look at the origins of belly button rings and why the ladies wore them. All of these things ties up with the woman's lib & Jezebel-spirit and unfortunately from a Christian perspective it is not ok.
If it was my daughter sitting on my lap asking me this question I would try to explain to her as gentle as I could that it is not the place of a Christian lady to get tattoos and belly button rings, but that is just me.
I was just curious as to whether or not you also feel the same about nose rings?
I don't know if you have a son or not, but would you allow him to marry a girl with a nose ring?
The reason I ask is because maybe you're not familiar with the story of Rebekah... the woman Abraham's servant Eliezer found to marry Isaac. The Bible clearly states she wore a nose ring because (Gen. 24) Eliezer gave her one as a gift and "put it in her nose". Not only that, he was obviously carrying nose rings with him while looking for the right young woman to marry Isaac's son, so they must have been fairly common in those days.
I totally understand it might not be someone's preference but when Christians start calling such things "the spirit of Jezebel", I always wonder if they missed this part of the Bible.
As for myself, the only piercings I have are one in each ear and they may as well grow closed because I rarely wear earrings or jewelry at all (in the type of work I do, any jewelry I wore would just get destroyed anyway.) I also don't have any tats and don't plan on getting any, but it's just my preference.
Ironically, my Dad is an ordained minister and my Mom got a tattoo around age 50. She said she'd always liked them and thought they were pretty. He really didn't want her to get one (not for religious reasons--he just doesn't like them) but they compromised and she has a small, colorful tattoo about the size of a quarter.
I don't mind tats/piercings on other people--I've seen some amazing works of art on others that I loved--but have no interest in it for myself. I am often drawn to tattoos on others because I find they each have a very interesting story behind them, and I like people's stories. I am also especially drawn to tattoos that were done in memory or honor of someone else. However, I HAVE seen some tats I'd consider obscene (nudity, sexuality, etc.) or demonic (gang signs, demonic faces and images) that I wouldn't be comfortable with at all.
In the end, to me, it just all boils down to the person and who they are.