I sold mineral rights that were inherited from my mother and was kept in an estate from 2010 until division/distribution in 2019. What date would be used for the FMV.

Per IRS Publication 551 (pages 9 and 10), the basis of property inherited from a decedent is generally one of the following.

1. The FMV of the property at the date of the individual's death.
2. The FMV on the alternate valuation date if the personal representative for the estate chooses to use alternate valuation. 
3. The value under the special-use valuation method for real property used in farming or a closely held business if chosen for estate tax purposes. 
4. The decedent's adjusted basis in land to the extent of the value excluded from the decedent's taxable estate as a qualified conservation easement.

Perhaps the estate administrator can give guidance on what date and value was used for estate purposes?

are these by any chance 'fracking rights'?  if so be careful as they had a very, very different value in 2010 vs. today.