It's difficult for me to imagine a Norse-dominated crusader state being set up anywhere in the Levant. None of the Scandinavian kingdoms really had the manpower to manage it, and this combined with the distance means that reinforcing this state with new arrivals from Scandinavia would be pretty much impossible. In any case, IOTL Sigurd "the Crusader" only launched his crusade because of the success of the Franks, and thus the KoJ was already established with no more room on the Levantine coast for a Norse principality. As for the Norwegians themselves, IIRC they were more interested in entering the service of the Byzantine Emperor than in remaining in the Levant, an obvious choice given the legacy of the Varangians.
A Norse lord under the KoJ, however, is easy to imagine. Sidon would be the obvious choice, as it was the city captured by Baldwin and Sigurd - just have Sigurd convince Baldwin to give it to one of Sigurd's kinsmen/nobles who desired to remain in the Holy Land instead of giving it to Eustace Grenier. That would hardly be a "Norse realm," however.