If the solar system is good and needs no major repairs a second storage tank would be best.
Test your system by switching off the heating element circuit to the hot water tank.
An electric water heater tank will do an excellent job for your coal water coil.
The solar tank is the #1 tank, it takes in the cold street/well water, the coal tank is the #2 tank and takes in the warmed #1 tank water.
Some valves to do the switch over between summer and winter will be needed.
During high summer operation the solar can heat both tanks and the coal will be off.
Late spring/early fall solar heats the #1 tank and coal will warm the #2 tank.
Winter solar just warms #1 tank and coal heats #2 tank.
If you have separate electric and solar tanks now plumb the coal coil to the electric tank as it should be #2.
If you have electric heat elements in the Sepco tank disconnect them and wire the new electric tank.
Some pictures of the current setup and more information regarding the current setup will get you more help.