I think Austria is really your only option, given the OP. You've ruled out France, Germany, and Russia as part of the question, and really there were good reasons why those powers came to the fore, or remained there in France's case, in the nineteenth century. I won't say it was inevitable, because virtually nothing is truly inevitable in history, but there were strong reasons for it. As for the alternatives you ask about, Only Austria has the potential, as I see it. Neither Italy or Spain have as much in the way of necessary resources as Austria. It's worth remembering here that Austria became a fairly highly industrialized nation IOTL, with quite a lot of industry. As I see it, there is a tendency to view Austria through the lens of 1918 and project that back to the entire history of the state. This leads us to ignore the elements of strength while placing too much emphasis on the weaknesses (which there most certainly were. I'm not trying to say Austria didn't have major internal faultlines, just that I think we need to re-examine our weighing of competing trends.). Plus, both of the alternative hegemons, Spain and Italy, have even more significant problems to acquiring regional dominance. Both are hemmed in by substantial mountain ranges, which isolate them from the rest of the continent. On the first hand this makes the need for a regionally dominant military less strong, because the nations are shielded, at least to a degree. The geography also encourages naval strength as both Spain and Italy are dependent on the sea for more of their trade and are more vulnerable to attack than Austria. They also have more to gain from naval strength, and I think, and easier time acquiring colonial territories. Additionally, Spain has incredibly strong internal divisions that need to be dealth with before it can become a regional hegemon. Italy, to my knowledge, doesn't have that problem, though I could be wrong, but it was relatively late to be united into a single state. Earlier than Germany, to be sure, but the factors I already mentioned lessen the need for a unitary Italian state to have a powerful army.
Honestly, I don't think Austria needs any truly major reforms to achieve this status, given the OP stipulates the OTL powers are weakened. Incremental reforms, leaders making better decisions, and perhaps a way to play other ethnic groups off the Hungarians (the Serbs might fit the bill and that could be achieved either through Austria never losing Serbia or by re-acquiring it in the nineteenth century) would be enough to eliminate Austria's largest impediments.