I was thinking more of a Prussian king marrying an Austrian princess.
Unfortunately for this idea there was a significant shortage of Hapsburg princesses by mid-nineteenth century. Emperor Ferdinand I had no children, and among his siblings by 1848 none were unmarried or had any children of age. Even going back a generation and then looking at the cousins of the Emperor, there simply weren't any eligible Hapsburg brides laying around. Even going back further and looking at second-, or third-cousins, there simply isn't anyone of value to the Prussian court. The best matches I can find would be Maria Christina of the Two Sicilies, Maria Anna of Savoy, Maria Cristina of Savoy, or possibly Louise of Orléans if the Hohenzollerns are willing to wait a few years - but none of them are 'Austrian' princesses, and they're likely to bring very few advantages to the table in Berlin's calculations.
On the Hohenzollern side, Frederick William IV married Elisabeth Ludovika in 1823 when he was still the Crown Prince. She was very influential in Prussian politics, and played a key role in Prussia's antagonism to Austria even prior to the Springtime of Peoples. This worked out perfectly for Frederick William, who was against both constitutional liberalism and the unification of Germany; in the latter's case he used his influence as Crown Prince in 1815 to prevent the liberals from crafting a constitution, and as to the former he was perfectly content to allow the Hapsburgs to continue to (in-directly) lead the German states through their influence. So you'd have to get rid of both the of them. Unfortunately the next in line, William I, was even more of a reactionary and anti-German as his brother; there's a reason he earned the epithet as the
Kartätschenprinz during the 1848 Revolutions.
Your best bet might be to butterfly a Hapsburg princess into existence - perhaps one of the many who died in childhood lives - and on the Hohenzollern side for William to choose to stay with his first wife, Elisa Radziwill, instead of leaving her in 1826 after his father, Frederick William III, argued that she wasn't an appropriate wife for a Prussian prince. This would remove William as Crown Prince, and make the third son, Charles, the Crown Prince - then making him Prince Regent, and finally King, if Frederick William IV's stroke happens as per OTL. Charles was noticeably more liberal than either of his two older brothers, as he had pushed for a liberal constitution, and after that defeat tried for several years to transform the State Council into a proper ministerial body. As well during the 1848 Revolution he spoke openly in favor of the Unification of Germany - which is largely why his role in government was considerably diminished after the reactionaries crushed the radicals. Charles' OTL wife of Marie of Saxe-Weimar-Eisenach would likely be considered too lowly of a match, and instead Frederick William III would have to look elsewhere. While he might pick William's OTL second wife of Augusta of Saxe-Weimar-Eisenach, he might also decide to opt for someone else. More like Charles and unlike his two eldest children, Frederick William III was a reformist, if in the Hohenzollern model, and wasn't diametrically opposed to liberalism - or to Vienna.
Once again though, there really wouldn't be an 'Austrian princess' for him to pick.
However, if you're willing to flout the idea of the reverse - a Prussian princesses and an Austrian prince - there's a bit more room to work with. Princess Louise didn't marry until IOTL 1825, just a year after Archduke Franz Karl's OTL marriage to Princess Sophie of Bavaria. However the Hapsburgs and Wittelsbachs had been planning the marriage of Sophie and Franz Karl since both were very small children, so it would take a considerable POD for Frederick William III's offer of his third daughter to be taken seriously. It is doable though - Saxony was considerably weaker than Prussia, and already in the Hapsburgs' sphere of influence, so another marriage wasn't required to keep the Saxons in line
per say. Also both Sophie and Franz Karl were both initially quite against the arranged marriage - there's always the possibility that they maintain this personal antagonism; though it would have to be on Franz Karl's part, as once Sophie decided she would marry him she was quite intent on the idea, and became (in)famous in both Vienna and Dresden for her attachment to the young Archduke (she would later become obsessed with the idea of placing on of her sons on the Austrian throne, and after young Franz Joseph became Emperor she was the power behind the throne in many ways for the early years of his reign). As well there's plenty of things that can happen outside of family politics to tilt things more in Prussia's favor. Sophie's father, Maximilian I Joseph, had done plenty to piss off the Hapsburg both during the Napoleonic period and afterward at the Congress of Vienna; he was lucky to get off with a kingdom at all. Maximilian I Joseph was virulently anti-German unification after his experiences in the Confederation of the Rhine, and it was largely on his lead that the princes of the smaller German states rallied against either a Hapburg-led re-constituted Holy Roman Empire or a Hapsburg-led federal union of the German states, leading to the OTL German Confederation. Perhaps, going down this route, a possible POD could be Maximilian I Joseph creating much of a stink over the Hapsburgs breaking their promise to him at the Congress of Vienna regarding the Baden Succession. Under Semi-Salic law Baden would have passed to Maximilian I Joseph's son and OTL successor, Ludwig I, upon the deaths of Charles (OTL 1818), and his uncle, Louis I (OTL 1830); both of whom were childless. However in 1817 Charles issued a new line of succession by which his half-uncle, Leopold I, would follow Louis. Charles followed this up the following year just months before his death by granting a liberal constitution which ensured the new succession rights. IOTL in 1919 the great powers, including Austria, forced Bavaria to accept the loss of Baden in the Treaty of Frankfurt; however lets say Maximilian I Joseph refuses to give in, and does something drastic like invade Baden to press his succession rights. The Bavarians would be hard-pressed to actually hold the Grand Duchy in the face of guerrilla warfare, even assuming they could defeat the Badners in the field; and once the powers, including Austria, intervened, as they would, it would all be over for Maximilian I Joseph. This would likely be enough to force the Hapsburgs to select another wife for Franz Karl, and Princess Louise of Prussia might just make the perfect match - the Prussians would likely be a key ally for the Austrians in the War of Badner Succession.