Although OTRCAT.com does not have recordings of every series listed below, the following is quick reference guide to old time radio show series, theme music title, and composer (when available).
"Kerry Dance, The" [aka: The Cuckoo] - Margaret Casson (m); J. L. Molloy (w)
Pot O' Gold - "Pot O' Gold (In The Air)" - Harry [?] Salter
Presenting Al Jolson (NBC, 1932 - 33) - " My Mammy" [from the 1918 vaudeville revue "Sinbad" starring Al Jolson] - Walter Donaldson (m); Sam Lewis (w); Joe Young (w)
Pretty Kitty Kelly - "Kerry Dance, The" [aka: The Cuckoo] - Margaret Casson (m); J. L. Molloy (w)
Prudential Family Hour, The -
Open Theme: "Intermezzo" [theme from the 1940 film "Intermezzo (A Love Story)"] - Heinz Provost (m); Robert Henning (w); (or it could be an Intermezzo by Brahms or Mascagni)
Close Theme: "Bless This House" (1932) - Helen Taylor; Maye H. Brahe
Pursuit of Happiness - "Of Thee I Sing" [title song of 1931 Broadway musical] - George Gershwin (m); Ira Gershwin (w)
Pulitzer Prize Playhouse - "Pulitzer Prize Playhouse" - Bernard ["Bernie"] Green (psuedonym of Bernard Greenwald)