I remember there used to be an option on WordPress to block comments from search engine indexing. I can't find it anywhere, though.
Does anyone have suggestions or alternatives? Thanks.
To my knowledge, there is no easy way to achieve what you want. What I think you would need to do is two parts:
Normally comments are part of the page (for content they belong to) and I don't think there are any conventions to block certain part of page from indexing.
At best you would need to separate comments to reside at separate URL from content and block indexing of such URLs via normal means (like robots.txt or meta tags).