We have a coleman evcon furnace. The furnace runs constantly. It'll get to the temperature but then the fan doesn't quit and it only blows out cool air the the reset switch pops up and needs to be be reset before it'll blow out warm air again.

It sounds as if your furnace is exceeding the limit tempperature of the manual reset switch. The coleman is designed for the fan to continually run when this limit switch is tripped in order to keep the heat exchanger cool.( it is a safety feature) afew things may be happening.
1. the manual limit switch( the one you have to push) may be defective.
2. The fan may be running at too low of a speed. Turn power off at circuit breaker. locate circuit board on the board there will be one terminal that says heat if the red wire from the blower is on it tthen you may need to up the speed. follow the wires from the blower to the board if it has multiple speeds then you can isolate the red and put the blue or orange on the heat terminal.
3. the board may have an adjustable fan on and fan off pin selector if it is set up to come on to long or go off to soon it may not be controlling the temp of the heat exchanger properly.
4. I would also suggest checking to see if the orifices and gas valve are set up for your sytem correctly.
these are just simple ideas let me know how things go.