And if you wanna go a little further out there... Sapphire
Sapphire is aluminum oxide, Al2O3. It has a compressive strength of 2 gigapascals, so even if you accept some losses in incorporating it into a biological composite, you're still starting out way ahead of natural bone. Aluminum is not currently know to play any significant role in biology, but it is bioavailable in ion form (e.g., as aluminum citrate) and accumulates in the biosphere, so it should be available in normal food supplies--and if biology can handle laying down oxidized iron crystals, I'm sure something can be worked out for depositing oxidized aluminum!
However, sapphires are a bit different from this. Sapphires are made out of corundum with traces of other metals in it, which, according to the Wikipedia section on synthetic versions of it, seems to require very high temperatures - in the thousands of degrees - in order to form; specifically, temperatures that seem incompatible with life as we know it. Moreover, some of those reactions require bases (which sometimes do doubleplusungood things to terrestrial biochemistry) or fluorines. This is different from goethite, for which I cannot find anything similar; goethite apparently forms when other iron-containing minerals are weathered, and does not involve high temperatures, bases, or the like. This is why limpets can use goethite to make teeth.
Now, I have no idea whether or not there's a way to make sapphires in a way that doesn't involve high temperatures, overly-acidic or overly-basic chemicals, or other conditions inimical to life as we know it, which is where you come in.
Is there, in fact, some kind of biological method - capable of existing within Earth-based biology - of producing sapphire, corundum or aluminum oxide bones?
Good answers will either explain how this is undoable or will cite some form of chemical reaction capable of doing this that can exist within a Earthly creature's body without melting them, burning them, corroding them, or otherwise doing something unpleasant.
The BEST answers will cite a chemical reaction that DOES involve high temperatures, basic chemicals, and the like, but said best answers will ALSO provide a way for it to work with Earthly life.