Deck posts and railings screwed to a single rim joist feel wobbly because the rim joist flexes whenever you lean against the railing. Adding blocking will stiffen the rim joist and make the railing feel much more solid.
First, tighten any loose bolts and screws. If the post doesn't have bolts, add them—carriage bolts work best.
Cut pressure-treated 2-by blocking (the same width as the floor joists) to fit tightly between the rim joist and the next joist. Place the blocking directly behind the post and toe-screw it into both the rim joist and the neighboring joist. Fasten additional blocking every 4 ft. along the rim joist.