Can be something original or something adapted from campaign.
I’d like:
All In. Replace Kerri with some sort of super-hybrid. Nydus and air attacks alternate. I really enjoy defensive maps.
Harvest of Screams. Alternating Frozen/Unfrozen, enemy attacks relentlessly during Unfrozen. Would be similar in theme to Dead of Night.
Supreme. Not a hero mission, but players must fight souped up versions of these fantastic boss fights.
I kinda want a map with supported AI where they seige the enemy with the player. For example, the Prologue of Protoss and when Artanist defend Raynor.
Avoid the AI path while completing objective or Defend allied AI while killing the enemy.
Ooh. Or that movie where you need to move Tosh through the map with Terran support.
This would be an interesting map to do. Hard to design though.
I liked the campaigns, but I think the replayability of coop is better. So I would like more campaign maps be turned into coop maps.
A whole new map type called Onslaught where you have to survive up to a certain wave or duration.
Map no. 1: Second Zeratul mission from WoL, where Maar comes at you, stronger and stronger every time. Side mission is to activate some structures by staying near it for a while.
Map no. 2: Fourth Zeratul mission from WoL where the Protoss make their last stand. Side mission could be the same.
Map no. 3: Protect the first spawning pool from Amon’s forces. Or just hold out there. Based on the HotS mission.
Map no. 4: The second Epilogue mission (Terran). Yeah. Just survive.
And I wouldn’t mind more defensive missions either.
Great ideas here, especially the Maar one.
The immediate ones that come to mind are…
Dark skies.
Kill count timer rewards aggressive play for players who prefer that to defending.
Larger area to defend means greater need for cooperation.
Bonus objective is just “Do your job better”
Third party allied forces make for a more interesting barricade than just a wall the bad guys chew on.
Valerian announcer.
What more can you ask for?
I’d really like to see a mission that is a time/score attack. For instance, the 4th WoL Protoss mission. It would be impossible to clear the map, because the enemies would spawn infinitely. Your goal would be to protect the Shrine until it can safeguard its data. If you hold out long enough (say 20 minutes) then you and your ally can retreat/win. Or you can choose to survive on the map as long as possible for the bonus XP. Bragging rights to whoever gets the most kills 
I’d like a map that has the Rip-Field generators from the Maw of the Void mission. All Rip-Fields must be destroyed to unlock the final “boss” area.
From the Campaigns in general, I’d like something like the various “reinforcement spot into objective kill” missions. One way to do this would be that they’re hard to get and help significantly but briefly; another is they’re granted at the start and help little but get attacked resulting in mission failure if too much is lost.
As far as more WoL goes, I’d most like to see Gates of Hell with rescuing X amount of limited friendly spawns, Supernova with forced movement into an objective kill, and In Utter Darkness with killing X enemies either in a time limit or while surviving or both.
From HotS, Supreme with killing a series of Zerg “bosses” seems awesome if viable.
I would like a proper genocide map. Kill all enemy structures except creep tumors.
And not with dead of night’s day/night gimmick. Just a standard 2vAI. Maybe ping the last structures when there’s only a handful left, like in outbreak.
Someone a while ago suggested “end game” be adapted to coop. That would be cool too.
I would love to have one of the Nova mission in chapter 3, the one that you fight against Alarak troop and deploy Gorgan BC.
This is tough because there are so many, but here are a few ideas I had.
The mission in Hots where you have to capture scourge nests to shoot down gorgons, except in reverse. Maybe there’s a chasm along the middle of the map filled with Zerg, and you have to work around it while destroying some sort of air defense so that the gorgon can clean it out before the fortress is overrun.
Colonist Evacuation from Wol, but with a few tweaks. I was thinking a map design more similar to Sudden Strike from Nova: Covert Ops would be interesting in this mission as if I remember correctly, that map was very hilly and made for a dynamic where control of the high ground mattered. For bonuses, it could be interesting to use the garrison mechanic from Nova Covert Ops as well, with the garrisons in strategic positions along the convoy route.
-The Moebius Factor. Basically unchanged from campaign version, replace Kerrigan with some sort of hybrid.
-Lab Rats. Similar to hand of darkness, except adjusted to make sense for co op. Essentially is just a mission to sterilize a hybrid creation facility.
A good holdout would be great. The variant on All-in that you suggested sounds really nice.
I’ve been toying with the idea of a Co-op version of In Utter Darkness, although there’s nothing playable yet. The main and bonus objectives have been reversed though, in that the main objective is to protect a Docking Bay (replaces the Archives) for about 21 minutes as it launches escape shuttles into the warp gate, and then the bonus objectives are to survive for an additional 3 and 6 minutes (you can let the Docking Bay die at this point), so some shuttles that are elsewhere can get to the warp gate and escape.
After that, you have the choice of continuing for as long as you like (quitting out won’t count as a loss). As for what you’ll face, to use a Protoss enemy as an example, you’ll face the usual attack waves, but also Hybrids, Vanguards, Wrathwalkers, Destroyers, Tal’darim Motherships (Tal’darim still aligned to Amon), regular Motherships, Annihilators, Dark Archons and, if you last long enough, a surprise!
Still some things to work out with the editor, like how to give new units their own AI (e.g. making Wrathwalkers kite and Annihilators use their cannons against high-value targets) and how to prevent a loss when you quit (after you complete the main objective).
I have to say I’m actively against a lot of these other ideas; I think we should avoid making such direct simple reskins of an existing mission.
Apologies for being blunt to its author, but I want to try to shoot down one idea in particular. I’d rather skip In Utter Darkness entirely than see it in the form Crane suggested. It seems like another with too much overlap, and the optional quit/continue is a novel idea but serves no real purpose and would be a huge mess in practice.
Salvation, In Utter Darkness, All In. More maps like temple would be awesome.
Blizzard doesnt need to wait to make some original idea for a new co-op map. Im more than happy with just destroy that or defend this. They don’t need to make every new map super unique like with P&P, Cradle of Death, and the Purifer one, a lot of people even seem have found the last two they made annoying because of their forced attempts to make them unique.
I’d much rather have like 50 maps that are similar in terms of objectives, but with different terrain and environments, than just the like 15 or so we got that are all uniqueish from one another.
Oh, no offense taken. It’s going to be something very subjective either way.