A concept for overriding parent theme JavaScript in a child theme.

child-theme.js

window.themeName = window.themeName || {};

(function( window, $, undefined ) {
	'use strict';

	// Override the carousel config properties.
	themeName.config.carousel.autoPlay = true;
	
	themeName.setupCarousel = function() {
		// Override the carousel set up without affecting anything else.
	};

})( this, jQuery );

parent-theme.js

window.themeName = window.themeName || {};

(function( window, $, undefined ) {
	'use strict';
	
	$.extend( window.themeName, {
		config: {
			// Default carousel properties.
			carousel: {
				autoPlay: false
			}
		},

		init: function() {
			// Initialize the theme JS.
		},
		
		setupCarousel: function() {
			// Default carousel functionality.
			// $( '.carousel' ).carousel( this.config.carousel );
		},
		
		setupGalleries: function() {
			// Default gallery functionality.
		}
	});
	
	$( document ).ready(function() {
		themeName.init();
		themeName.setupCarousel();
		themeName.setupGalleries();
	});

})( this, jQuery );