You can buy followers, views, likes, and comments for Instagram accounts of all types, both private and public. However, it will be more effective if your account were public because it will be easier for visitors to your profile to view your content and take further action.
When your account is private, the user cannot know what kind of content you create to follow, like, or comment, if they are not following you. In short, public accounts attract followers easier than private ones do.