1) yesterday's newspaper but yesterday morning (why not - yesterday's morning)
2) this morning's newspaper but a morning newspaper (why not - a morning's newspape)
I'm not sure that I, or indeed anyone, can really tell you 'why' usage has developed in this way, but the simple fact is that possessive 's' is not appended to the words 'yesterday' and 'tomorrow' when they determine nouns that denote times of day (morning, afternoon, etc.), while the 's' is obligatory where they determine other, ordinary nouns.
As regards the nouns 'morning, afternoon' etc. themselves, when they function as
modifiers (i.e. typically following an article), they are, like adjectives, invariable, and therefore do not take the possessive termination. When, however, they form part of a
determiner phrase (as in
this morning's,
yesterday afternoon's...), the possessive termination is, once again, obligatory.