After getting many creative responses to my question (thank you!!!), I finally figured out a solution to my balcony railing problem. Riley liked to stick out too far between the rails and perch her feet on the other side! Last night, she fearlessly walked through the rails and then traipsed along the 5 inch walk on the other side of the railing!!!
Needless to say, I figured out a solution first thing this morning.
I went to Walmart (nice & quiet on July 4th morning, btw) and browsed the garden section. I purchased plastic "chicken wire" and some cable ties. It was only $10 for a 30' roll that I was able to cut down and fasten to the railing. 45 minutes later I was finished!
Here are some pictures. It really isn't an unattractive solution. I trimmed up the plastic mesh so it looks neat, pulled it taut, and trimmed the cable ties.