I found a solution on the WordPress forums, if anyone is trying to do the same thing here is the solution: http://wordpress.org/support/topic/custom-read-more-text-wrapped-in-a-div
I added the following to my functions file:
function wrap_readmore($more_link) {
return '<div class="post-readmore">'.$more_link.'</div>';
}
add_filter('the_content_more_link', 'wrap_readmore', 10, 1);
Thanks,
Josh