In a similar fashion to Clerics, both Divine Champions and Blackguards MUST have a patron deity, and MAY NOT be "faithless". Their power has to come from someone. Unlike Clerics, however, they do not have to be within "one step" of their patron deity's alignment. In fact, the only alignment restriction that Divine Champions and Blackguards have are the base requirements of the Prestige Classes themselves.
Also, perhaps somewhat obviously, since Divine Champions and Blackguards do not get Domains, they are not limited in their choice of a patron deity in terms of available Domains unless they also have levels of the Cleric Class.
Heironeous and St. Cuthbert do not have Divine Champions (per the prestige class), as their holy warrior servants are all Knights of The Last Stand (use the Paladin base class in that case.)