Is it possible to create Warp Signs that can only be used every hour in Minecraft Essentials?

Alternatively, you can use the CommandSigns plugin to achieve this.

This assumes that the dungeon can be reached with /warp Dungeon and standard players have no access to it via the commands; only signs.

Firstly, the ~ identifier allows you to place a limit on the sign, and the ^ identifier executes the command under the player's name, but with the '*' permission node.
Note that this does not give them full command permissions, only just for the sign's execution; command stated in the sign.

You can visit the BukkitDev Wiki page for more information.

Here's how you set it up.

1. Place a sign, you can color it, make it fancy - Do whatever you want.
   Just ensure it doesn't follow Essential's sign formatting.
2. Enter the following command in the chat: /cmds add ~3600
   This defines a sign, with a execution cooldown of 3,600 seconds (or 60 minutes).
   Except, your sign does nothing.
3. Right click (or punch) your sign that you want this to be applied to.
4. Enter the following command: /cmds edit and punch the sign that you created in Step 2.
5. Enter the following command: /cmds insert 2 /^warp Dungeon.
6. Punch/right-click the sign.
7. You're done.

Check out the plugin BoosCooldowns on the Spigot website. http://www.spigotmc.org/resources/booscooldowns.2759/

You would want to create a cooldown timer for the signs.use.warp command.

This is a plugin you have to purchase to get the latest version but it is continually updated. I have seen older free versions on some webites but I think it only cost $3 and it is worth it. I use it for numerous commands and it is easy to configure per player or group.

You can do this in vanilla by using a scoreboard objective. Create the objective using: /scoreboard objectives add time dummy time and make the sign that teleports you out set @p's score for time to 0: /scoreboard players set @p time 0 and have whatever teleports you to the dungeon test to see if the score is the minimum required (60, when using a one-minute clock) by using this command: /testfor @p[score_time_min_60]. Make a hopper coming out of that command block into the one that teleports you to the dungeon. To increase the score each time you exit the dungeon, use a one-minute clock with a command block at the end with the command: /scoreboard players add @a[score_time_min_0] time 1