Buy 10 LM317, you'll use them.
The point of a voltage regulator is to maintain a particular voltage no matter what the circuit connected demands. In real life this is up to a point, and this point is 200mA in your example. Also in your example you want to maintain 9.1V (from the zener) with up to a 13.7 input voltage. In this case R is simple to calculate V=IR, I = 200mA, V = 13.7-9.1, R = 23 ohms. No getting around that if you want 200mA into your circuit. If no current happens to be consumed by the connected circuit, then 200mA is going to have to be run though the zener. Since P=IV, that means 200mA is going to have to loose 9.1V through that zener, or 1.8W. The absolute maximum dissipation of the BZX559V1 is .5W with a 25 degree environment, so you're going to need a bigger zener.
Hopping over to Digikey, I put in that I want a single zener, qty 1, in stock, voltage from 9-10.5V, and a wattage of something like 1.5W-5W. Sorting by price I have two options: A $.52 (CAD) 1SMA5925BT3G 1.5W 10V SMD zener or a $.53 1N5925BRLG which is thru-hole. Looking at the thru-hole one, you see it can totally dissipate 1W at 50C ambient. But we need to do 1.8W. Hmmm. Looking at the SMD one, we see it can totally do 1.5W when it's leads are 75C, but can only really do 0.5W when the environment is 25C. Another hmmm.
Maybe we can solve this for more money. Get a 1N5346 for $.64. This can dissipate 5W according to the datasheet if we magically keep it's leads at 25C. But really since the junction to lead thermal resistance is 25C per watt and it would be pretty optimistic to get another 25C per watt out of the leads themselves, it's going to be pretty hot. We are running now around 9.5V with all that current going through the zener so that'll help. But maybe this can work. The resistor will need to be (P=V^2/R) (13.7-9.5)^2/23 ohms = 0.78W. Fortunately resistors don't care too much how hot they are so a 1W or 1.5W one will probably do. Check the datasheet of course!
Compare all this to a TO-220 package LM317 which from Digikey costs $.84 for a genuine ST one. It can handle this all day long, and has a convenient screw hole which you can use to affix it to a heat sink if you need to help get rid of the heat. Also you can set it for exactly the voltage you want. It'll even shut down if it gets too hot.