I think European History itself (until WWI) was a giant Habsburg wank (with a few hiccups here and there), but if you want to make it to the 20th Century (and if we are talking about the House of Habsburg-Lorraine as the Austrian branch as well):
Some of this may be ASB, I'm not sure but....Austria unifies Germany instead of Prussia (in fact the Hohenzollerns are spanked). That alone might do it. Allies to do so come from other places. If necessary, have the other anti-Napoleon Allies and Alexander I of Russia agree to keep Napoleon II as Emperor of France with Marie Louise as Regent which would entail a near permanent alliance (for a several generations at least) with France. Or kill off Nappy before he loses so the infant Napoleon is acclaimed anyway. Austria and Metternich would be fine with such an outcome if Marie Louise can still have power over the boy. Austria leads the charge to unify German with Napoleon gone (one way or another) instead of being resistant.
Pre or post German unification Austrian Germany is separated from the rest of the Habsburg domains (Hungary-Slavonia mostly, possibly Bohemia) and is ruled separately (only retaining the same head of state) or with two different Habsburg monarchs sitting on different thrones (one Habsburg German Emperor another as King of Hungary). No federation or union. If this challenge is really about the Austrian Habsburg line in general, I would just put several members of the dynasty over different national thrones instead of one all encompassing Emperor from Vienna.
With the agreement and urging of the other Great Powers, the Grand Duke of Tuscany (Habsburg) exchanges his domain to take the throne of Moldavia/Wallachia and the Duke of Modena (Habsburg) exchanges his Italian domains for an independent Polish kingdom taken from lands from defeated Prussia. In exchange the House of Savoy forfeits further irrendenist claims on Habsburg territory (Trentino-Aldige/Trieste/Croatian coast) and sphere of influence (Albania) and have to make a military pact. To gain Russian support, Austria supports them in the Crimea and joins them in dismantling the Ottoman influence in S.Eastern Europe. Austria claims Bosnia earlier and Germanizes and fills it with settlers. If necessary Serbia is annexed or made a Croatia like sub-kingdom to prevent what is going to happen in 1914. It never gets its own royal house. Russia gets Bulgaria (with a Romanov ruler?), Greece as a sphere of influence, and Thrace and Constantinople (its great dream) for its support. If the Hungarian nobles eventually make trouble as they do in OTL then at this point the Habsburgs have enough force to crush them entirely.
Going into the 20th Century the Habsburg empire (and its cadet branches) are ruling present day Germany (in a system much as in OTL but with the Habsburg dynasty instead of the Prussian Hohenzollern) and Austria, parts of Poland, Romania, Hungary, possibly Albania (at least sphere of influence) and are allies of Russia, Italy and possibly France (depending on who is in control there). WWI is averted and thus the Fall of Eagles never happens and they continue to reign (if not rule, given natural democratization) over most of Europe. OTL Dr. Otto von Habsburg is still born as Emperor/King Otto founds some version of the EU, introducing a single currency across all Habsburg reigning domains and creating an economic superpower.
However if the Lorraines are not considered Austrian Habsburgs, alternatively just have a male Habsburg survive past 1740 - the line of one of the younger sons of Ferdinand III perhaps, or either Joseph I or Charles VI have a son and heir. No Pragmatic Sanction, no War (and loss of Silesia) and Prussia remains a minor power. The House of Habsburg-Lorraine (or in the case just Lorraine) may still exist but none of its heirs are anything more than Viennese courtiers or heirs of a French-occupied duchy. I would also have Baltasar Carlos of Spain live (and marry Marianna as planned instead of her father) and spawn at least one more generation of healthy heirs to butterfly OTL War of Spanish Succession and the compromises that entailed, also whatever it would take to get the Habsburgs out of Italy since that was nothing but a quagmire for them for centuries. They should concentrate on Germany or barring that S.Eastern Europe in the wake of the weakening of the Ottomans.