Heat of dilution for NH4NO3 aq. sol. can be retrieved from: "International Critical Tables", Vol. V, 1929, p. 162.
Dear Michael: please note that, considering Hess's law, we get the same final thermodynamic state, by either considering the neutralization of NH4OH (aq) with HNO3 (aq); or by considering the same moles of NH4NO3 as directly dissolved in water, for equal final concentration. The signalled thermochemical data concerns to last path.
Here, the last two contributing parcels can be derived from the enthalpy of aqueous dilution for NH3 and HNO3 (corresponding to steps i and ii), while considering also the enthalpies of formation of the relevant pure compounds. The first parcel can be derived from the enthalpy of aqueous dilution for NH4NO3, i.e., that corresponding to step (iv):
ΔHf[NH4NO3 (aq)] = ΔHs[NH4NO3] + ΔHf[NH4NO3(s)],
where ΔHs[NH4NO3] denotes the enthalpy of (aq.) solution that can be retrieved from the before mentioned reference.