I am also trying to find out information about a Malarky family in Glasgow.
I have 2 different spellings for the surname - Malarky and Millarky - so I am not sure which one would be the correct one. It could also be that your spelling is also linked to the same family.
My link is for an Ann Malarky, who was originally married to a John MacReadie and then (probably?) married a James Kerr. It is through this second marriage that I have an interest.
Ann was a fish hawker and her first husband was a cattle drover. I can find info about Ann, but am finding nothing about John MacReady, other than he died in December 1874. I am guessing that they may have been from Ireland and moved over to Scotland, but this is purely a guess. I have been advised to look for a connection in Sligo, Mayo or Galway as possible origins as this seems to be a common location for this family.
Ann was born BEF 1858 and died BET 1876 and 1898.
She stayed in Glasgow. I can't find any wedding or death details about her but she was called Ann Kerr on the wedding certifictae of her son (Michael Kerr to Janet Winchcole) so I am again guessing that they eventually did marry.
The only family I have found is for the above mentioned Michael Kerr (b 3/1/1876 in Glasgow) and Ann was listed under her maiden name of Malarky, although James Kerr is listed on the birth certifictae as the natural father.
Does any of this ring any bells with you. Could this be the same family that you are looking for?