seems Facebook changed the result of posts, few weeks ago it was possible to read the comment count from the post directly
https://graph.facebook.com/125909647492772_502
This works perfectly with me:
fields=shares,created_time,comments.summary(true).limit(0)
This return comments count at summary
and return 0 comments at the same time which is perfect as you only need the comment count.
You can do such requests:
{pageid}/posts?fields=comments.summary(1){id}
It will return a list of posts including comments count of each post. Here I have returned only the comment id because I only need the number of comments per post, but of course you can include many other fields:
{pageid}/posts?fields=comments.summary(1){id,message},id
You can get total comment count via FQL. See this question below as reference:
Facebook API - comment count via FQL
Here's the query you need: SELECT comment_info FROM stream WHERE post_id = ...