Attaching a link to the MO website with death certificate for Thomas Dunn, which gives his parents' names, if you don't have that yet. Maybe other information that will help too.
Do a search here, and be sure to give the year 1931, makes it a little easier.
And also spell it Dunn (not with the "e" on the end) or it won't come up.
http://www.sos.mo.gov/archives/resources/deathcertificates/