The coelacanth, the shark and many other living species have not changed in over a hundred million years. Yes, some species are fairly stable. But your claim is that all species are stable. Giving a few examples of stability is not evidence for your proposition, especially given the numerous counterexamples. Indeed, by implicitly accepting modern interpretations of the fossil record, you have opened the door to the counterexamples.
Do you even believe that any fossils are that old?
Since the coelocanth has come into discussion again, I thought I would note that there's no evidence that the coelocanths of today could reproduce with the coelocanth of 100 million years ago. The fact that you cannot distinguish these by their skeletal morphology does not establish procreative compatibility. There are numerous species today which would look indistinguishable for all practical purpose from some very closely related species were they both fossilized. In other words, the coelocanth may be an almost uniquely stable species or it may be a species undergoing minimal evolution of the sort that hasn't discernibly changed its morphology. Either (or both) of these statements would apply in that present population (they would not apply to the entire population of primordial coelocanths because the groups which did indeed evolve would no longer look bear any resemblance to a coelocanth).