I'm sure a lot of people would agree that punishing falcon kick or whatever B move is the best way to handle a spammy low skill Captain Falcon--or any other character, for intent and purpose. I think you should practice shielding and/or spot dodging your cousin's attacks that are easily punishable, such as Captain Falcon's B moves. Using a jump to avoid the Falcon Kick is possible, but it might make the window to punish your cousin's falcon smaller than you want, so I think your primary concern is learning how to space properly. If you know how to position yourself so that falcon's down B ends right before reaching you, you can punish it for more damage than if you had to chase after him (jumping, spot dodging, shielding). Rather than only having enough time fort an aerial or a dash attack, you could hit him with a smash attack that make the punish hurt a lot more. Just please keep in mind that this advice is based off of the play style I can assume your cousin uses from the post you made. Trying to position yourself based on your opponent using Falcon Kick wouldn't help you at all versus a more competent captain falcon (Jumping and spot dodging would be a very poor choice when trying to avoid a Falcon on a higher level of play). . And, of course, I'm not a genius or expert at Project M or Melee, so the advice of someone else may be better than mine.
To sum it up--No character or specific move will counter your cousin's play style more than the the way you play against him.
Edit: I'm assuming that you're playing defensively. Falcon Kick spam wouldn't be a problem if you kept pressuring him with attacks.
