I think you're a bit confused about the tools you need to solve this problem. If I'm following you correctly, you are looking at a boiler that runs off of diesel and it is heating water, that in turn, heats your house via steam.
The specific heat capacity (~1750 J/kg K) of the diesel is largely irrelevant to this problem, unless you're designing a preheater to the boiler. The outlet for this side of the boiler does not contain diesel fuel. The diesel is consumed in a reaction, and (for all intents and purposes) CO2 and H2O are produced. The specific heat of that mixture can be found by taking a simple mixture of the gases produced using a combustion equation and something like C12H23 as a decent stand-in for diesel fuel.
If I were looking at this, I'd first want to know the lower heating value (LHV) of the diesel fuel. The LHV is the heat of combustion, minus the vaporization energy of the stoichiometrically produced water. This basically tells you how much heat is produced by the diesel and is available for exchange, assuming 100% efficiency. This value will let you know how much water you are able to vaporize and use to heat your house.
For a quick back of the napkin calculation, you can take the LHV of the diesel and assume an 80% or so thermal efficiency. That's about typical for most process boilers, but it could range from 50-90%, depending on your specific model.
