How can I make it so that when I change my Facebook profile picture, it won't appear on my friends newsfeed, but could still view it if they went to my profile.
There is no direct option to do this. But there are some way.
Hide the post from your timeline immediately.
Click on View Activity Log from you profile (a tab on cover photo) and hide the post from your timeline by clicking pencil symbol.
Other thing what I can thing is when you are adding a new profile picture select audience as Only Me and after few hours you can change the audience. It will not show the change in friend's newsfeed.