Ok, so I've just got a new emerald version, and I've been trying to trade all my pokemon from my FR to it, so I can have Charmander etc. Whenever I try this it tells me that the other person's pokemon can't be traded at this time.
What does this mean? And why does it appear? Any help would be appreciated.

Have you completed the quest on the Sevii islands so you can trade to Hoenn from Kanto? Check the main site first. That will help.

have you fixed Celio's machine in FR? I believe that you also have to unlock trading in Emerald, though I'm not sure what you have to do (maybe get the National Dex?)

Yes, you need the National Dex in Emerald as well, by beating the E4 the first time.

Ah, that's a shame.

I had completed the game in FR though, but I traded to sapphire so I could start again on FR.
Shame, I wanted to pretty much do the entire game with my team. Evee, Electrike, Squirtle, Treecko and Poochyena. Ah well, thanks for helping!