How do you auto-activate plugins from child themes

include this function in your theme and use this hookfunction

wp_register_theme_activation_hook($code, $function) {
    $optionKey="theme_is_activated_" . $code;
    if(!get_option($optionKey)) {
        call_user_func($function);
        update_option($optionKey , 1);
    }
}

functions and examples:

<?php
/**
 * Provides activation/deactivation hook for wordpress theme.
 *
 * @author Krishna Kant Sharma (http://www.krishnakantsharma.com)
 *
 * Usage:
 * ----------------------------------------------
 * Include this file in your theme code.
 * ----------------------------------------------
 * function my_theme_activate() {
 *    // code to execute on theme activation
 * }
 * wp_register_theme_activation_hook('mytheme', 'my_theme_activate');
 *
 * function my_theme_deactivate() {
 *    // code to execute on theme deactivation
 * }
 * wp_register_theme_deactivation_hook('mytheme', 'my_theme_deactivate');
 * ----------------------------------------------
 * 
 * 
 */

/**
 *
 * @desc registers a theme activation hook
 * @param string $code : Code of the theme. This can be the base folder of your theme. Eg if your theme is in folder 'mytheme' then code will be 'mytheme'
 * @param callback $function : Function to call when theme gets activated.
 */
function wp_register_theme_activation_hook($code, $function) {
    $optionKey="theme_is_activated_" . $code;
    if(!get_option($optionKey)) {
        call_user_func($function);
        update_option($optionKey , 1);
    }
}

/**
 * @desc registers deactivation hook
 * @param string $code : Code of the theme. This must match the value you provided in wp_register_theme_activation_hook function as $code
 * @param callback $function : Function to call when theme gets deactivated.
 */
function wp_register_theme_deactivation_hook($code, $function) {
    // store function in code specific global
    $GLOBALS["wp_register_theme_deactivation_hook_function" . $code]=$function;

    // create a runtime function which will delete the option set while activation of this theme and will call deactivation function provided in $function
    $fn=create_function('$theme', ' call_user_func($GLOBALS["wp_register_theme_deactivation_hook_function' . $code . '"]); delete_option("theme_is_activated_' . $code. '");');

    // add above created function to switch_theme action hook. This hook gets called when admin changes the theme.
    // Due to wordpress core implementation this hook can only be received by currently active theme (which is going to be deactivated as admin has chosen another one.
    // Your theme can perceive this hook as a deactivation hook.
    add_action("switch_theme", $fn);
}

for more information see this post