On FindMyPast and the IGI I have found 2 children possibly belonging to Mary (Ann) ATKINS.
James illegitimate child of Mary Atkins at Seighford, Staffs, bap. 14 Jul 1839
and
William son of Mary AITKINS at Lane End, Staffs, bap. 02 Sep 1841
How likely are these two to both be the children of Mary? Are Seighford and Lane End in close enough proximity in these times?
Mary POSSIBLY had a daughter called Ann but I can't find her.
She was transported to Australia and arrived in 1847 "with a child" but other than that I have no details.