The Harald who was father of Godred is not identified in the primary sources, but the king of Limerick of that name seems like the most likely individual. In the list of the kings of Man, NHI (vol. 9, p. 466) suggests that the Harald who was father of Godred might have been Harald of Denmark (son of Gorm the Old), but this seems unlikely. Some would include a certain Magnus, also a son of Harald, as another king during this period, but it is likely that this is a mistake. The existence of a Magnus son of Harald is given only in late sources, and seems to be a error for mac Arailt in the earlier sources, in which mac became Maccus and then Magnus in successive corruptions of the records. In further support of this, observe that the personal name Magnus is based on the Latin word magnus (great), and, if we are to give any credence to the account of Heimskringla, the name derives more directly from Charlemagne (Carolus Magnus in Latin), with king Magnus 'he Good of Norway being the first individual of that name. This would seem to exclude the possibility that a Viking bore that name as early as the tenth century. While it is possible that Maccus is a corruption of some other Scandinavian name, it seems much more likley that the mac Arailt who appears in the annals was the son of Harald about whom we already know, i.e., Goffraid mac Arailt.
Note: Harald (Aralt) is referred to as the grandson of Ivar in AI. CS calls him a son of the grandson of Ivar, i.e., of Sitric (Aralt mac .h. Imair .i. mac Sitric, Rí gall Luimnigh, do marbad la Connachtoíbh). If the account of CS is literally true, and the grandson of AI just means descendant in general, then Harald would probably be a brother of Olaf Cuaran, as shown in the table. However, Ivar also had a son named Sitric (d. 896), so if the mac .h. is a mistake for just .h. (a common abbreviation for the word ua [grandson] and its various declensions), then Harald may have been son of this earlier Sitric. (Stewart Baldwin, Isle_of_Man_kings_Baldwin.htm). (My comment: If Sitrick was dead 896, he was not the father of Harald, who was borned about 916).
P.A. Munch antar att Harald Svarte av Islay, kung på Söderöarna (Hebriderna) 1035-1040, var son till kung Godred Haraldsson. Munchs teori är också att Harald I Svarte var fader till Godred Crovan, som var kung på Man och Hebriderna 1079-1095. Om man följer den norska traditionen, refererad också av Munch, blev Harald Svarte uppkallad efter sin farfar Harald Gudrödsson och Godred Crovan efter sin farfar Godred Haraldsson. (Fra Skanke-släktens historia, stamtavla 1a, G.V.C. Young, 1986).