How Can I Correctly Attach new 4x4 Deck Rail Posts on the surface to an existing deck?
There are plenty of options, but none are pretty. Also, you may need to add sub-decking framing members to support such brackets.

To steer clear of (off-topic) product recommendations, I'll instead suggest this: Mount your posts to the inside of your rim joists, through the decking. You'll get a more solid railing and it'll look better. It'll look something like this (you'll probably need to use lag bolts from the inside of the posts, into the joists):