With a P.O.D. of 1815, create a unified German state that is significantly more liberal than the German Empire of OTL.
1848 would indeed be key here, for the reason @LSCatilina pointed out. As the Vormärz showed, Germany had a large and by that time progressively minded middle class.
With a PoD which leaves the 1870/71 unification and constitution unchanged, though, I´d say liberalization is not so easy anymore, as large parts of the bourgeoisie have, by then, agreed to be co-opted by the agenda of Prussia`s elites. Many here and elsewhere speculate on WI Friedrich III. had not died of cancer in 1888, he was renowned to be more liberal. I´m slightly skeptical here, but it might still be a possibility.
an entry from July 1885 tells us that he met with Bismarck and had agreed to keep him as chancellor in the event of his succession.
How do we get Germany to be centralized, like France, unlike the OTL german federal empire?
Indeed that would prevent the OTL split between nationalism ans liberalism. When the founding myth is the overthrow of all authoritarian regimes rather than the victory of one of them.Get 1848 to succeed...somehow. As I take it, the kings of both Austria and Prussia were highly reluctant, and the movement fell apart.
I beg to disagree. Prussian has a long history of liberalism e.g. in religious freedom and the Nazi ideology didn't originate in Prussia either. The problem was that Germany ended up ruled by autocrats who successfully suppressed liberalism and (temporarly) the SPD - but not that those autocrats happened to be Prussian.1848 is your best bet really. A Prussia-unified Deutschland will have a much tougher go of it.
I don't see the need for that. Many anti-liberal countries are centralized and many liberal aren't.How do we get Germany to be centralized, like France, unlike the OTL german federal empire?