Apprenticeship; proprietorship; friendship; childhood; falsehood;
Using your examples it is seen that ship carries the connotation of status. One's status is that of an apprentice, proprietor, friend, and so on. As a mnemonic we could say that ship (as in cartaging or transporting) has commonality of derivation with the suffix, -ship, in that one is carried by (and, conversely, carries) one's status.
Childhood, falsehood, statehood, on the the other hand, harks back to hood as a kind of covering, cloak, or insignia. A pre-adult is "covered" by the state, the cloak, of being a child. A falsehood could be said to be the cover adopted in lieu of openness or honesty. Using those general guidelines for coining a "hoodship" (neologism) word that is not already taken should stand you in good stead, but with no guarantee that no overlap in ultimate meaning cannot be found.