While my PoD is before 1800, there's not a lot of change in Europe until the end of the Napoleonic Wars.
Based on a map Susano created, where Prussia got Belgium, I have the Prussians taken down a peg in 1830, and severely annoying the rest of the German states. So, no Zollverein based on Prussia, which really helped them cement their position. Also, the map gave Silesia to Austria (no, we've never been able to figure out why), so at the end of 1830, Prussia has lost Belgium, the Rhine Province, and basically united everyone else in Germany against them. They still have Westfalen, with e.g. Essen, as a major industrial center, but they've lost their other two (Belgium and Rheinprovinz, iTTL; Rheinprovinz and Silesia compared to OTL), and they're economically weaker due to the developing customs unions excluding them, rather than based on them.
So, 'Germany' will end up mostly unified (eventually, hasn't happened yet, still working on this stuff), without Prussia - or Austria, which is why I say 'mostly' unified. I use 'kleinstdeutsch' as opposed to OTL's 'kleindeutsch' Reich.
I think that knocking them down a peg, and getting the rest of the German states legitimately worried about Prussian aspirations is a necessary condition for a non-Prussian based union. Beyond that, it may need for a little luck to go to the Non-Prussians...