So, my city bylaws state no open burns are permitted without a burn permit (a new permit needed for every fire..), and defines "open" as "where the flame is not wholly contained". This includes mostly-containing fire containers like chimineas. 

How would you design a charcoal forge where the flame is fully contained? 

I'm sort of thinking about modifying a small charcoal bbq, both for appearances and because you can throw a lid on it.

I would call any sort of forge fully contained. Flames do not leave extremities of the forge pot for charcoal, coal or coke use, same for gas units. No different than a gas stove top.

Best bet would be to ask officials, in an anonymous manner, what those codes entail for what you’re wanting to do. Tell them you’re planning on building a forge and maybe even provide some detailed drawings. Inform them of the number, types, and locations of your fire extinguishers in proximity to the forge and see what they have to say. 

Of course you could build a gas forge and not have to worry about it. 

May not want to use the word forge or build. 

If they allow a BBQ then you may slip under the radar. Find an old weber type grill and add a fire pot, brake drum, rotor, etc in the bottom. Cut a slot in the side to insert in metal into the fire. When your finished forging put the food grill back in place, and cover as you normally would.

If they allow a chiminea then you can build a circular container with a short chimney. Use a small opening in the front to add fuel and or metal.

What ever you use, make it fancy, paint it with fresh paint, and grill a hot dog ever now and then so you can say yes, I use it for cooking food.

Don't forget to paint your anvil a bright colour so you can call it 'art' if questioned ... Spots or stripes and a face for bonus points 

May have to consider a shed. At that point treat it as a fireplace. 

Sometimes I wish I lived in town or at least on the outskirts. Then there are times that I thank God that I live in a rural area especially when I hear stories like this.

"'Tis easier to beg forgiveness than ask permission..."

Tell "em it's a BBQ grill and you like your meat smoked with coal rather than hickory.

Tell them the anvil and hammers are for tenderizing the meat. And you like it really tender.  

I like the forge in the bbq grill idea. 

The question is: do you have neighbors that will be annoyed by the hammering and cause issues? Will it be out in the open or in the back yard? 

Whatever you do do it safely and keep a fire extinguisher handy just in case and to ease the minds of anyone that does see it. 

Yeah, it'll be out in the open in a backyard. 

Re: building a gas forge, I'm uncertain as to the regs in my locale regarding unrated, homebrew propane devices built by a person who isn't a qualified gas fitter.

I wouldn’t trust a gas fitter to build a gas forge... inspect it maybe, and then I would prefer a HVAC or appliance man. 

What do they allow? We are assuming they allow charcoal grills and gas grills? 

 

Aha! "No permit shall be required for commercially produced out door appliances burning charcoal, propane, or natural gas that conforms to the Canadian Standards Association" (CSA) codes and standards".

Methinks the charcoal barbecue is the way to go...

Edit: Alternately, though the price is steep compared with making my own, I can buy NC Tool forges through a Canadian farrier supply company. Anyone had experience?

Going off the wording of that quote I'd say a coal or Coke forge would work since coal and coke are not " charcoal, propane, or natural gas"

An, Gene, other way around. That says their is an exemption for what is in the US “UL” rated wood, gas or charcoal appliances. Dose the CSA also cover building codes? If so a home built solid fuel may qualify as a fireplace. As esentualy that’s what it is