First of all, the Wall is a world apart. News often reaches them very late. It has been said a number of times by a number of people.
"It is not," Pycelle admitted, "but none of Mormont's men have
returned as yet. Marsh fears the wildlings have killed them, and that
the Wall itself may be attacked next." He fumbled in his robe and
found the paper. "Here is his letter, my lord, a plea to all five
kings. He wants men, as many men as we can send him."
"Five kings?" His father was annoyed. "There is one king in Westeros.
Those fools in black might try and remember that if they wish His
Grace to heed them. When you reply, tell him that Renly is dead and
the others are traitors and pretenders."
"No doubt they will be glad to learn it. The Wall is a world apart,
and news oft reaches them late." Pycelle bobbed his head up and
down. "What shall I tell Marsh concerning the men he begs for? Shall
we convene the council . . ."
ASOS - Tyrion IV
"The Imp?" Davos did not understand the question. "He is at King's
Landing, condemned to die for the murder of his nephew."
"The Wall is the last to learn, my father used to say. The dwarf's
escaped. He twisted through the bars of his cell and tore his own
father apart with his bare hands. A guardsman saw him flee, red from
head to heel, as if he'd bathed in blood. The queen will make a lord
of any man who kills him."
Davos struggled to believe what he was hearing. "You are telling me
that Tywin Lannister is dead?"
ADWD - Davos I
Secondly, GRRM deliberately tries to avoid providing a time frame when writing.
The reason I am never specific about dates and distances is precisely so that people won't sit down and do this sort of thing.
My suggestion would be to put away the ruler and the stopwatch, and just enjoy the story.
So Spake Martin -
So we can't really make any assumptions about the timeline and infer from it the date when Aemon dispatched his birds and when were they received by their intended recipients.
Now thirdly, Davos did not read the letter right away. It was received by Lord Alester Florent when he was the Hand of the King and he told the Maester that the King won't want to see it. After Lord Alester's downfall and his appointment as the new Hand to replace Florent, Davos Seaworth chanced upon the letter while learning how to read and immediately realised the gravity of the words.
His first duty was to help his king rule, and for that he must needs
understand the words the ravens brought. The best way to learn a thing
was to do it, he had found; sails or scrolls, it made no matter.
“This might serve our purpose.” Pylos passed him a letter.
Davos flattened down the little square of crinkled parchment and
squinted at the tiny crabbed letters.
Davos suddenly realized just what he was reading. He turned the letter
over, and saw that the wax that had sealed it had been black. “This
is from the Night’s Watch. Maester, has King Stannis seen this
“I brought it to Lord Alester when it first arrived. He was the
Hand then. I believed he discussed it with the queen. When I asked him
if he wished to send a reply, he told me not to be a fool. ‘His Grace
lacks the men to fight his own battles, he has none to waste on
wildlings’ he said to me.
ASOS - Davos V
Now that proves that the letter arrived right after the Battle of Blackwater Bay which happened a few weeks after Renly's demise. For all we know, it might be that Wall never learnt about Renly's death at that time. The fact that they knew of Robb's and Balon's coronation doesn't mean much. The Wall is in the North and anyone might have had sent the word forward that the North has a King again. Robb himself may have sent a raven forward to tell Jon. What we do know is that Lord Mormont knew about Robb's coronation and told Jon before they went on the Great Ranging. As for Balon's coronation, it was immediately followed by invasion of the North in the name of the Iron King of the Isles. Winterfell was sacked and burnt, and the Watch knew what happened down there in their neighbourhood.
Highgarden and Storm's End are however very far down in the South. News if any was sent their way, would have reached the Watch the last. Also note how long it took Davos to learn about Tywin's death, an equally important (If not more) event, he may not have learnt about it at all had he stayed at the Eastwatch. We know for certain that the Watch knew about Renly's coronation, but when did they learn about his death? We know they knew of it by the time they very electing Mormont's successor but when exactly? It is possible that Lord Tywin's reply may have informed them of that development (In which he subtly hinted that he favours Janos Slynt for new Lord Commander - That played a role in the elections) but explicitly? We do not know.