The death was reported in the Dundee, Perth, and Cupar Advertiser on 24th June 1856 and in the Dundee Courier on the following day. I haven't access to the articles themselves, but the index to the Courier says:
"Melancholy Accident - A melancholy accident occurred on Friday last at Cranistoun quarries, whereby a young man, named Alexander Aitken, was deprived of life. It seems they had undermined the quarry too far, when the bank above gave way, and buried the ..."
The article may not go on to give any clue about family.
The only possibility I can see on FreeCEN is Alexander Aitkens, 30, labourer, not born in county, at Ferry Street, Montrose.