Works, but always adds more button, even if there's only one paragraph.

auto-read-more.php

<?php
function the_content_readmore($more_link_text = null, $stripteaser = 0) {
	$content = get_the_content($more_link_text, $stripteaser);
	$content = apply_filters('the_content', $content);
	$content = explode("</p>", $content);
	foreach ($content as $key => $value){
		if 	($value != null || $value != ''){
			if (  !stripos( $content[$key], '<iframe' )  === false ){
				echo $content[$key];
				for($i = $key+1; $i < count($content); $i++  ){
					echo $content[$i];
					if 	($content[$i] != null || $content[$i] != '') break;
				}
			}
			else{
				for($i = $key; $i < count($content); $i++  ){
					echo $content[$i];
					if 	($content[$i] != null || $content[$i] != '') break;
				}
			}	
			break;						
		}
		else echo $value;
	}
	echo '<a href="javascript:void(0);" class="button button-more">Read More <i class="fa fa-lg fa-chevron-circle-down"></i></a>';
}

This function creates a custom excerpt and tacks a "more" button on the end. The excerpt is limited to a single paragraph, or an iframe (embedded video) and a paragraph. The problem, is that the "more" button is shown at all times, even if only one paragraph exists.

Line 8. Do you intend to say "There is no iframe" OR "Doesn't start with an iframe" ?

Total rewrite but this should do what you want: https://gist.github.com/kerihenare/9557715