Here are 4 1960's TV comedy shows about the Navy.

An episode of ABC TV's BROADSIDE, starring Kathy Nolan, Shiela James (from Dobie Gillis), Arnold Stang (Top Cat), Dick Sargeant, and Edward Andrews.
The show title is The Monkey's Paw. It has a very funny Ghost scene, and Arnold Stang is always crazy funny.

An episode of NBC's Mr. Roberts starring Roger Smith, and guest star Edward Byrnes (This 77 Sunset Strip for both), and Richard X Slattery. 

An episode of Hennessy starring Jackie Cooper and Abby Dalton. They visit the USS Arizona Memorial at Pearl. While most of these episodes are
straight comedy, this one really brings out the tears and patriotism. It may have been a sort of a booster for donations, to the Arizone Memorial,
which was still under construction at the time.

Finally, an hour long Wackiest Ship in the Army starring Jack Warden and Gary Collins. It has some comedy, but some tense moments as well.

All in All, two hours of high seas comedy and adventure, with shows you dont see any more.