We looked at several homes here with identical fireplaces, and were told they were coal-burning fireplaces.

Yes, those kinds of fireplaces generally burned coal - depending on where you are they may well have burned lignite, which is a sort of in between peat and bituminous coal.

The solid panels are a nice touch to have, still. Many times they've simply disappeared. The ones on Mom's fireplace (I'm about 95% certain hers had one) are long gone, possibly to a scrap drive during World War II.

I'd love to see pictures of your fireplaces.

We have a 1918 bungalow that had 2 of these fireplaces when we bought it. They were back-to-back, but not see through. As you noted, these boxes are very small but we were able to "steal from Peter to pay Paul" and enlarged one box enough to convert it into a wood burning unit, and plan to convert the other side to a vented gas coal unit in the next few weeks. We've also uncovered another one of these fireplaces (a previous owner and removed it) and are currently restoring it to add a gas coal fireplace at the same time. You might check out http://www.gascoals.net/ - the Victorian Fireplace Shop - they have tons of information on these direct vented units on their website and have been very helpful to us. good luck!

We also have an old home with double sided coal burning fireplaces. Mantel in one room is marble and wood on the other side in another room. We do not want to destroy the mantels or the face and interior baskets of the fireplace. We realize it is not safe to use and the chimney has been partially dismantled from the roof to the floor in the attic. We would love to convert these fireplaces to wood burning, gas is not an option in our area. If anyone has any suggestions we certainly would appreciate the help!
Thank you.

Why not just buy some good bituminous lump coal and use that? It's what they were designed for. Additionally coal is safe to use in older unlined chimneys, as it does not produce any flammable creosote (liners initially came into favor because they reduced/eliminated creosote seepage through the soft mortar joints of older chimneys - when there was a chimney fire the flammable creosote with a low ignition temp that had soaked through the porous mortar would ignite not just on the inside of the stack, but on the outside as well thus igniting the home). It is likely that there is a coal source in your area. Coal is less expensive than burning firewood (unless you cut it from your own lands), doesn't spark, doesn't produce flammable creosote and requires much less frequent tending - a 5 gallon pail full of lump coal will create a bright cheery fire most of the day. The covers on your fireplaces would improve the efficiency for heating, however, they were always a pain to deal with and are difficult to use once the fire has gotten hot; for a recreational fire I would highly reccomend leaving them off (this is why they are so hard to find - most people didn't use them even back then).

Here is a link that might be useful: scroll to the second post down - demonstraition of a fireplace coal fire

Just a quick note for your information concerning older chimneys. When your chimney was build it may not have a clay flue tile lining. It would be a fire hazard to use any chimney before it has be lined with an approved chimney liner. Whether it be wood, coal or gas venting the heat transferring to the surrounding structure can burn your house down. This means the wood surrounding the chimney can spontaneously combust due to the high temperature. Get a certified chimney sweep to evaluate your chimneys potential for the type of use you are considering.