Christian saxon kingdom rules over Germany.

Surviving Ottonian dynasty, perhaps. Their powerbase was in Old Saxony (and, indeed, they invested heavily in the growth and expansion of the eastern frontier, that is, modern Brandenburg), and were champions of Catholic Christianity. Even by whatever butterflies you want the HRE survives through the Middle Ages under the Ottonids, and Italy somehow falls out of their grasp - like it did with the Lombard League v. Frederick Barbarossa - then the remnant German-HRE will be likely centered around Old Saxony (I use this term to encompass modern Hannover, Braunschweig, Saxony proper and possibly Brandenburg, if it never becomes an autonomous duchy).

An even more interesting and earlier PoD is to have the Saxons Wars of Charlemagne be much less brutal and result in a peaceful Christianization of Saxony. I remember from the top of my head that after the first Frankish victory, most of the Saxon lords had admitted Carolingian suzerainty, were baptized and so forth, but Widukind's effort reinflammed various rebellions against Charlemagne, giving into almost twenty years of conflict. IOTL, the native Saxon aristocracy was decimated, and the country was effectivelly annexed into Frankia, only regaining its autonomy much later, with Emperor Ludwig the German. If Saxony converts more peacefully, like the Bavarians, Poles, Czechs and Danes did, it's possible that they retain their local autonomy, even if integrated in the Frankish sphere of influence. As soon as the Carolingian Empire falters, they might exploit the power vaccuum to enforce their domain over Franconia and Frisia, for example.

I know these PoDs are a bit early, if you want something post-1000 or 1500 A.D. I have no idea.
 
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