James Cronin and Mary Margaret Sullivan

I'm looking for information on James Cronin and Mary Margaret Sullivan.  I'd love to find out more about them, especially who James' parents were, so I can continue this branch of my family tree.  Here's the information I have.

James Cronin

• Born 15 Jun 1860 in Listowel, Ireland
• Died 05 Apr 1927 in Cook County, Illinois
• Death certificate lists Mary McNamara as his mother, but that's Mary Sullivan's mother
• Emmigrated to the US in 1883
• Married Mary Sullivan in 1886 (in Chicago, IL)

Mary Margaret Sullivan (possibly Margaret Mary Sullivan?)

• Born 8 Oct 1863 in Kerry, Ireland (not sure if it was Listowel)
• One source lists her from Skehenerin, Listowel, Kerry, Ireland
• Died 13 May 1932 in Cook County, Illinois
• Death certificate lists Michael Sullivan and Mary McNamara as parents
• Emmigrated to the US in 1881