I have seen a variety of birds in various positions inscribed on tombstones and have written about them before. Birds represent a variety of things, including resurrection, innocence, and peace.
Recently I saw this pair of parakeets, aka budgies, on a tombstone.
I do not know that parakeets have a symbolic meaning but I suspect these parakeets indicate that the deceased had a fondness for these cheerful, friendly birds. She probably even had several parakeets herself.
These parakeets likely tell us a little about the deceased and her love of parakeets.