Too bad that others did not even try to reply the actual question, and focused only on saying how much they dislike the "cogito ergo sum" argument.
Indeed, it is an argument, not an axiom, but its conclusion "I exist" is what is indubitable, not exactly in the sense that you cannot question it, but that you know that you know it, with absolute certainty, without any chance that it can be wrong.
Unlike what Ram Tobolski said, the "causation principle" is not the second indubitable believe, I am still hoping to ever find an argument as magnificent as "cogito ergo sum" but for causation, but it seems that none has ever found it, and it is also not what you are looking for.
This is what I have understood. The "I exist" belief has an empirical component, the argument "cogito ergo sum" is logically valid, but I know that it is also logically solid —that means, that actually the conclusion is true— only if I know that the premises are true, and I know that the premise "cogito" is true, empirically, because I am thinking at the very moment I am questioning myself about all this, and I know it.
So the "second indubitable" belief, like "I exist", would be "I think", actually, and the others, independently of the order, would be actually any phenomenological experience I have, such as "I am seeing a coloured form", "I am feeling pain", etcetera. Why? Because even if the world does not exist and all that, the experience I am having is still happening, and I cannot deny that I am having some experience, with some qualities.
This is the basis for many other philosophical systems, such as the phenomenology of Husserl, and some theories of Bertrand Russell, and of the Vienna circle, about sustaining all knowledge on logic, while gathering the information these indubitable experiences give. However, they are not at all the only ones that have observed this, and you can find this in many many others.
Of course, the particularity of Descartes, and that most of these others philosophers neglect, except perhaps Husserl, is that he is not only accepting those phenomenological truths, but he is also questioning whatever is not as certain as that, specially the existence of the external world. The others take advantage of these true believes, but assume plenty of other things, therefore polluting the indubitability of their theories.