You probably need to define a new loop function for the Custom Post Type to pass to the render parameter.
As in the example from https://jetpack.com/support/infinite-scroll/
/**
* Add theme support for infinity scroll
*/
function twenty_ten_infinite_scroll_init() {
add_theme_support( 'infinite-scroll', array(
'container' => 'content',
'render' => 'twenty_ten_infinite_scroll_render',
'footer' => 'wrapper',
) );
}
add_action( 'after_setup_theme', 'twenty_ten_infinite_scroll_init' );
/**
* Set the code to be rendered on for calling posts,
* hooked to template parts when possible.
*
* Note: must define a loop.
*/
function twenty_ten_infinite_scroll_render() {
get_template_part( 'loop' );
}
As you can see you can call a template part within that function to generate the next load of posts to be displayed (Infinite Scroll will update the query for you so you simply need a loop template.)