I also have trouble finding coal of any kind, as well as iron.
If you don't have access to metals and really need armor, massacre your puppy population and make leather armor and shields.
You also don't need to go into the caverns to access the GMS. Just dig straight down, walling off any breaches and diverting your staircase where necessary.
I could get some of them into copper gear, but is that enough to reliably fend off goblins?
In my experience, goblins are incredibly weak. A single dwarf in a full suit of copper armor with 2 layers can waste an entire goblin siege.
They are still training right now,
level 4 axe dwarves, level 6 fighters, level 1 shield users
which sucks, they've all had shields and bucklers for a long time now
they have no dodging to speak of..despite the numerous dodging demonstrations they've watched.
usually if a dwarf caravan or human one comes in, they'll take out the current goblins and I can grab a few pieces of wood.
I did breach a cavern earlier, so I'm getting some cap now, but it's growing VERY slowly. I can't even make bronze, I haven't found Cassiterite. I've got one guy in mostly armor pieces I've put together, and I think I can give him a steel axe that I bought, but half of them are still naked. I've been throwing wooden armor from the slaughtered elven caravans onto them just to give them some armor user practice.