I think the best way is to read up on latter Austrian military reforms and push them through earlier.
In general most reforms in this period, was focused on a few elements. Change from musket to rifles, changes to conscription (increase the number of conscripted soldier and the years serving) and logistic. Of course I think that Austrian problems wasn't military even if their command sucked, but their infrastructure. Much of the German success came from their ability to move troops fast to the front, feed them and replace them. The Austrian problem was twofold between 1814-1848 the Austrian Empire grew stagnant, the reforms they had been through before and under the Napoleons Wars was stopped, and Austria's neighbours outgrew them. After 1848 and until 1918 the Austrian hit a new problem, while the Prussian economic policies focused on the state develop the infrastructure (canal and railroads) necessary for economic developments, the Austrians embraced the Austrian school, which focused on letting private actor develop the necessary infrastructure against the state keeping the taxes low. The result was that the Austrian infrastructure stayed rather underdeveloped outside border regions to Germany and the Austrian core.
So a way to improve Austria is in the aftermath of the Napoleon Wars keep pushing some reforms through. A start could be the removal of serfhood in Galicia and Hungary mixed with a land reform. The result would be the birth of an rural middleclass, which would increase both tax income and push the creation of light industry. Of course it would also lower the production of cash crops and the export, but the increase domestic demand and tax income would more than make up for lost tariffs. It would also have broken the back of the Hungarian aristocracy.
The Austrian school was to large extent adopted because most money in the Austrian empire was made from agricultural production (which was exported on the Danube) or from the mining and industry in the border regions. As such there was little interest among the rich to raise taxes for infrastructure, because they had little need for it. With the development of light industry for domestic demand, there will be a greater demand to develop the infrastructure.