How many gallons of hot water from water coil?

The stock coil is 3/4" stainless pipe. To fit the cut outs on the stove back, two 18" pipes with two 90* el's with a 6 inch nipple making a U shape in firebox fits the stove just right. There are clips on the side of oven for it.
The optional stainless tank on the back is 25 gallons and makes too much hot water with a coil added, unless used as the only hot water source. It is not pressurized, and vented with two lids. So it will over humidify the home with coil. It sits on the stove top edge and is just right without coil for hot water in the kitchen (along with domestic water heater) and humidifying the home. It also takes advantage of the first section of stove pipe radiation since the tank is almost against the pipe all the way around it. Amish designed for their use without water under pressure, and used as the only hot water source, so it's an experiment to size the tank.

Factors are how hard you burn the stove for the area you're heating. Domestic hot water, or hot water space heating? (thermostat possible to control fire for circulating radiant if UL rating on stove is not required) Insulated tanks?

3/4 tubing with no reduction in pipe size at fittings circulates fine going into coil at bottom and out at top with raised tank. It even circulates with baseboard a floor above stove with 3/4 tubing all the way. I set one up with 10 lb. regulator and expansion tank that does not need a circulator at all. I added valves to throttle it back on warmer days since it circulated too much. If the relief valve opens a lot with your btu output, you'll have to increase tank size until it's right for how you burn it. (or decrease fire if you have a secondary heat source) Since it's our only heat source, we need to burn it as hard as needed, so hot water output varies. We use the oven daily, shutting it down after supper and coasting until reload at bed time.

I'd try a 50 gallon tank first. I don't think you'll notice any firebox cooling unless you run the cold water fill close to the return line at the coil. Cold should go into the tank, and ideally have a plastic pipe extending into the tank to act as a mixer.
Since the left side of the oven is slightly hotter than the right, it shouldn't effect oven temp much. But with the oven on, most of the heat from the fire goes directly sideways under the oven, so you get minimum heat to the coil with oven on.

Notice there is a full size brick across the front below door. Not a thin firebrick like the rest. It's a firebrick the size of a common brick. If replaced with a thin brick, this gives room for another U coil across the front. The thick bricks keep the front panel cool to prevent cooking your legs when standing in front of the stove. Canning is the only reason we wouldn't want to go with a thinner brick there since that's the most time consuming thing we do standing in front with it burning hard for hours. That's the only time it overheats the house. But that's due to canning at harvest time that's before heavy duty heat is needed inside yet.

We would be lost without the intake thermostat I added behind ash pan. (posted pictures on other threads) The stove builder told me he installs them for many Amish families and the women love them. (it's not an option sold to Englishers since the stove looses it's UL rating - but it works good for coal as well) It kicks up in the morning within seconds and if we only open the T-stat door partially, it closes by itself if we're busy without overheating.
Thermostat would be a great help if you need lots of hot water. The front air adjustment works like an idle for low burn when the T-stat is closed.

The optional summer grate is 10 inches above the grate at firebox bottom, so it will not heat the coil. We cook on it in the summer with short kindling only, and open the stack bypass slider as soon as we're done cooking. We also remove the lid to expose the bottom of pan to the fire to cook very fast. So it doesn't get hot enough to heat any water anyway.

The thermostat is a bimetal spring with an eccentric linkage in a housing used by Hitzer. (another Amish stove maker in Berne Indiana). It's called "Dual Heat Regulator". Woodmans has replacement part stock # 75TC. It does not come with the door / flapper or intake inlet. I fabricated that from a piece of 1/2" thick steel tubing cut on about a 45* angle and a piece of sheet metal for the door. I bolted it with angle iron brackets to the stove back.
The holes were in the flat sheet metal plate I used. I think it was a part from the inside of an old microwave......... Just scrap I had nice and flat. I cut a slot horizontal and made a small tab bolted onto the air intake for it to pivot on. Gravity closes it, adjustable chain comes with thermostat I believe. It's an old stainless toilet type.
Hung T-stat an dlet chain hang to find center of hole to cut at ash pan level. Holes to sides are for mount bolts. I used no gasket material since the half inch wall of tubing made good metal to metal contact.
Size of square tubing should be no larger than square inch ID of factory air inlet holes of air adjuster on door.