Railing modification is a very common issue with older apartment buildings. Chances are that if your property was built prior to 1985 your railings are not up to code.
Railing width between bars should be less that 5 inches. Bars should be vertical and NOT horizontal (horizontal bars create a ladder effect that children can climb).
Here are some common solutions:
#1 Wire Mesh
Wire mesh can be welded to the current railings. This is the recommended solution since this will last longest and is most secure.
#2 Adding Bars
Adding additional bars to reduce the spacing between rails.
#3 Wood Lattice
Wood lattice might look best with wood railings.
No Chicken Wire or Plastic Garden Fencing
These are cheap materials that don't last very long. They may also not suffice to insurance company requirements.