Bras, yes.
Coconut, no.

Kill an animal, skin it, wear a strip around the chest, wash the strip in running water at least once a day, replace every two weeks or so, call it good.

Oh, and Spuddly? Clothing serves many purposes*. While the mechanics will not protect any bonus to AC, in concept and in real life, clothing does help protect the skin. I am not saying that I would want to run through chest-high thorny bushes all day, but if I did, I would rather have some clothing on rather than going naked.

* Modesty, to keep warm, to keep dry, to display status, and for fun. Oh, yes, and for protection, already mentioned. And yes, most of those reasons are impractical for these gnomes, I already know that.