The line "Whoops, Mr. Moto! I'm a coffee pot" probably does allude to the Mr. Moto character of film.

As for the Java Jive song itself - "I love coffee, I love tea. I love the Java Jive and it loves me ..." I thought it may have been inspired by the children's rhyme/song that starts out similarly.

Wikipedia (at the moment) says: "Organ Grinder's Swing is a song composed by Will Hudson, with lyrics by Mitchell Parish and Irving Mills, published in 1936. It became associated with the Jimmie Lunceford orchestra. [1] Hudson based the "Organ Grinder's Swing" on the nursery rhyme "I Love Coffee, I Love Tea". [2]

Java Jive was written later:

JAVA JIVE lyrics
Ben Oakland and Milton Drake, 1940"