Can you be more specific with a model for the heater? On the Hayward website their heaters shown
here and
here all start at 150,000 BTU input. There are some Jandy models that are 125,000. Anyway, if I use their Table 2 from their manuals and scale from 150,000 to 125,000, they say that a 125,000 BTU/hr heater would heat a 1154 square feet of pool surface area pool by 10º above air temperature in the coldest month of use. Your surface area is 254 square feet so the heater could heat the pool around 55ºF above air temperature so it sounds more than enough for heating, but their table is for in-ground pools and isn't very conservative. Also, this assumes the heater is on 24 hours a day though they do assume the pool is uncovered and that there is some wind.
Assuming you have a 4 foot pool depth (leaving 4" between top of pool and water level), then your pool is 1018 cubic feet or 7600 gallons which is around 63,400 pounds of water. It takes 1 BTU to raise 1 pound of water 1ºF. If I assume the gas heater is only 85% efficient, then it would heat the pool by around 1.7ºF per hour. The real unknown here is the rate of heat loss from your pool. That will depend on the insulation around your above-ground pool, whether you use a pool cover, the temperature you keep your pool, and the temperature of the air during the day and at night. Lots of factors here.
If I look at average monthly temperatures in Winnipeg (which is in the province of Manitoba) shown in
this link, and if I assume you plan to use the pool during June through August, then the lowest average day temperature is 27ºC (80.6ºF) while at night it is 12ºC (53.6ºF). This is not much different than the temperature where I live in San Rafael as shown
here, but only for July through September. I have a 16,000 gallon in-ground pool but have a mostly opaque electric safety cover and keep the pool heated to around 88ºF using solar. If I had no cover, I would lose around 4-6º overnight and around 1-2º during the day. Let's figure worst-case 8ºF loss over 24 hours. That translates into 63,400*8 = 507,200 BTU needed so 507,200/*(0.85*125,000) = 4.8 so say 5 hours of heating over 24 hours. So your propane tank capacity should be enough such that it stores enough propane between visits (you didn't say how often the tank gets refilled) so that it handles around 500,000 BTU per day usage which is
roughly 23 pounds propane (roughly 5.5 gallons) per day. If you were to use a pool cover, then this usage would get cut by at least half if not more. For a thin cover like I have it cuts losses roughly in half. With a bubble-type cover, you could cut energy need to 1/4th compared to uncovered, but that assumes good insulation around your pool walls.
Consider this a VERY rough estimate that can be significantly affected by the factors I mentioned. I'm sure your propane supplier has experience with sizing tanks for pools if they are common in your area.
