I think well have to re-write a bit of history because during the earlt 11cen. Magyar was invaded and a puppet Magyar prince enthroned, all ties with the pagan steppe were lost. So maybe you should leave knights out of the Magyar equasion.

so no christianised cavalry?.

Cavalry

Magyar units should be:
Cavalry.
Magyer Tribesmen (rather like the Scythian nobles very fast and very powerful bows) and Kabars (exactly the same as Khazar horse archers)
to
Arpad Aristocracy(stronger and more decorative version of Magyer) and Székely (Rugged Hunnic peoples, semi-civilised looking, amazing firepower greater than the longbow) and Avars (Mailed horse archers, almost as powerful as the Székely )
to
Carpathian Riders/nobles (the people round the carpathians held on tightly to Magyar tradition) these people are just a re-vamped version of Arpad Aristocracy.
Pannonian Avars, these are the westernised descendants of the steppe Avars and are armed with lances and armoured with chainmail and a Frankic helm.
fejedelem, these are powerfull landowners and each one is the head of a Magyar tribe, they were followed into battle by the best of the best (heavily armoured Magyars carryind a bow and curved sword, they would be like Frankish knights except faster and carrying a bow and curved sword).
Kende , this is the supreme chief of the Magyars, he was important because only he could keep the tribes unified, he would be followed into battle by ten hand picked Fejedelem (these men were armed with long lances and curved swords, they would also be wearing Frankic type armour but with a little Magyar design in it.)