A solenoid is certainly the cheapest and easiest thing you can make yourself. Plus, it's not difficult to direct the flow of the water this way. You don't even need to make a valve. All you need to do is to re-direct the flow of the water.
Since you have a flexible tube, you simply need to move the end of the tube between two positions. In one position it squirts the water down, and in the other position, it squirts the water into a drain.
You can wind the solenoid coils yourself. Just cut lengths of steel rod, and wind coil wire (enamelled copper wire around them).
Push the end of your water tube into a short length of steel tube. The springyness of the water tube will hold it away from the solenoid, and allow water to flow into the drain (This is also the fail safe position. When the power fails, it will drain). When the solenoid is energised, it will attract the tube, and allow the water to flow down and be seen.
You may find that the flexible tube doesn't actually work well as a spring. In that case add a spring. Or, use a fairly long piece of thin steel tube instead of the flexible tube. This will be flexible enough to move the approx 4mm required.
Bad datasheet?
You should be aware that the datasheet linked is most likely not the correct one for the valve you will receive if you buy through that link. Various user comments and even the official description suggest this.
Wrong architecture?
This is not the right type of valve for your application:
Note: This is not a gravity-feed solenoid. This means that you will
need enough water pressure to fully open the valve. Check the
datasheet below for exact details. It operates at a minimum of around
3 PSI
Your application (coffee maker) is most-likely gravity-fed. That means you have a tank of water and you let it out into your machinery for use driven solely by its own weight. With this valve, you will not be able to fully drain the tank. As the level gets lower, the pressure on the valve will decrease to the point that the valve won't open.
If you are using this valve you will need a pump on the tank-side of the system.
Wrong forum?
The detail of mechanical actuation and pressure systems is probably better handled on one of the mechanical engineering or physical sciences forums.
Best Answer
As answered in the comments, your power supply is not sufficiently powerful to supply the needed current. Current required is cumulative for device's in parallel, so you must add the needed current numbers together.