migrate comments from old database to new database

I recently created a new WP site with some of the same content from my old WP site.

Is there a way to migrate comments from my old database to me new database? i tried importing old the wp_comments table into my new db via phpmysql. They did import and appeared in my wp admin, but they weren’t associated with the correct posts and categories. Looking at the .sql file I’m guessing that this didn’t work because the old comments all have different comment_post_IDs from my new db.

Is there a way around this or another way to migrate the old comments?

You could export all of the posts from your old site, including comments. Then, import them into your new site and delete the posts you don’t want. This will preserve all of the links between posts and comments.