If coexecutor-beneficiary of taxable Estate wants to purchase the family home at appraised value which is significantly lower than market how do you determine fair distribution without wasting to tax?

The appraised value is supposed to arrive at fair market value. Remember that property owned by a decedent gets a new basis, which is equal to the value as of the date of death. When a buyer purchases the property for its value, there is no capital gain or loss. If the buyer pays less than fair market value, then you can simply allocate the difference between FMV and the purchase price to the buyer's share of the estate.