Is it permissible for a married Jewish couple to be buried in the same grave, assuming the first to die is buried deeply and covered with stones as a barrier and then the second is buried on top of the first?

Shalom U'vracha, It is permitted for the couple to be buried in this way, according to Halacha. What is needed is a barrier between the bodies of 6 tefachim, which is approximately half a meter. (See Chazon Ovadia - 1:431 and Igrot Moshe- Yoreh Deah 442-444). All the best!