The events of season 5 of Agents of SHIELD prevent Coulson from taking part in anything that happens during Endgame.
TL;DR: Coulson is (finally! again!) dead in the MCU, before Endgame takes place. He was also no longer SHIELD Director by this point, and SHIELD is effectively (again!) defunct, so wouldn't be much use in the battle.
An important subplot of season 5, particularly the latter half, is that Coulson
is dying, and in order to prevent the future the team travelled to, they may need to let him die.
In the final episode of the season, The End, Simmons gives Coulson some of the Centipede serum, which was established early in the series as a (flawed) super-soldier type drug. For Coulson, this is
a cure (although possibly temporary), but
he hides it and gives it to Daisy (Skye).
(Daisy needs it for the super-strength, not as a cure).
At the very end of the episode, we see Coulson and May in Tahiti,
where Coulson is content to spend his last days in peace. It is established that he has only a very short time left.
Season 6 of SHIELD has Clark Gregg playing a different (as far as we currently know) character, Sarge, who happens to look exactly like Coulson. It's not clear yet, but presumably Sarge has no reason to fight in the Endgame battle, or to
attend Tony's funeral.
Given that both Season 5 and Endgame are time-travel stories, it's tricky to place everything, but episode 20 takes place at the same time as Infinity War, as there's an explicit comment that Thanos is attacking the Earth right then. Episodes 21 and 22 follow on directly from episode 20, and are before the
'snap', and certainly well before the latter events of Endgame.
(I haven't seen Season 6 yet, but I understand it's set a year after Season 5, which should put it between Infinity War and Endgame, but I understand that because of scheduling uncertainty they couldn't reference anything that happens in Endgame, so I'm unclear how the 'snaps' link into the show. However, I don't think that impacts Coulson's status).