The most reasonable course of action would be to consider the cost or other basis as equal to the sale price - what you were able to sell it for within a year of the owner's passing is as reasonable an estimate of FMV on date of death as anything else.
Unless the local real estate market was particularly active (or volatile), the FMV probably didn't change much in the one year that passed between the owner's passing and the sale. You can get verbal confirmation of this from a local realtor - ask for information on changes in the local real estate price index.
The fact that the tax-appraised value was higher supports this approach; if it had been lower than what you sold it for, the IRS could reasonably believe you had a gain on the sale. @DavidD66 stated, assessors are strongly inclined to over-value property for the purpose of increasing tax revenue.
@incumbent
