[Knight of Gondor]

I think it was just elements of Gimli's Dwarven personality that strike us as funny. While legions of Uruk-hai are pouring into the Deeping Coomb, Gimli is taking pride at his one-by-one elimination. (The contest itself was kind of amusing, and it was direct from the book.)

His pride was a little insulted when Aragorn dryly remarked "I suggest you take some rest and recover your strength."

He was a bit annoyed that his Dwarvish stamina was failing him in Emyn Muil, hence his frustrated remarks "Keep breathing! That's key!...Breath!" and such.

His own dry humor in the throne room of Denethor ("Certainty of death! Small chance of success! What are we waiting for?") was just his own "bring it on" attitude.

What other comic relief are you talking about?