Only way is CB Privacy and blocking the user. If User A blocks User B then User B can't post on User A's profile or comment on User A's posts. Beyond that it's possible to inject custom access checks using CB Auto Actions using the activity_onCommentStreamCreateAccess trigger, which is fired when checking if someone can create a new comment or not on a comment stream. Example of how to use it as follows.
Global
Triggers: activity_onCommentStreamCreateAccess
Type: Code
User: Self
Access: Everybody
Conditions
Field: Custom > Users
User: Action User
Operator: Is
Users: COMMA_LIST_OF_USER_IDS_HERE
Action
Method: PHP
Code:
Output
Display: return
If that function receives a false boolean it will deny access. In this case if the viewing users user id matches the list of user ids supplied it should return false and deny comment access.
Currently this would block commenting for all comment streams. If you want it to be more specific add the following extra condition.
Field: Custom > Value
Custom Value: [var1_id]
Operator: Equal To
Value: STREAM_ID
Replace STREAM_ID with the comment stream id you want to check against. It's also possible to check against asset. Example as follows.
Field: Custom > Value
Custom Value: [var1_asset]
Operator: Is REGEXP
Value: /^article\./
This would block commenting on any comment streams with an article asset.
Note that trigger will not fire if the user is a CB Moderator as they're exempt from create restrictions. It also cannot be used to allow access where they otherwise would not have access. It can only be used to take away access.