Vibration pattern matching
What you want might be way more complex, than you think, depending on your exact requirements.

The vibration sensor activates with any small vibration. It is not capable of distinguish different sources of the vibrations. The only pattern, that you might be able to look for with it, is a special pattern of multiple activations, as the coin jumps over the surface (depending on the max activation frequency of the sensor). Obviously this error prone.

Using a microphone to record the direct sound can give you more information about what happens. But that can get very complex very fast:


You need to measure the voltage from the microphone (which needs a suitable amplifier) with a sufficient samplerate (at least 2 times as fast as the highest frequency, that you want to measure). A high quality microphone might also need a better ADC (Analog Digital Converter), than the Arduino has build in.
The pattern recognition is another problem. Basically you have 2 ways:


You can look at the target sound signal and look for a few special properties of that signal, for which you can test the signal (for example a specific pattern of peaks above a threshold. Then you can test with some if statements for these properties, which is relatively easy. Though this is still very error prone.
You can train an AI to recognize the coin sound pattern. Though this is not a job for an Arduino, especially not for the Uno. You should use a special AI board for that. Though this is off topic here.



Which way you want to use depends on your exact requirements. When the recognition with the vibration sensor is sufficient, just use it. But we cannot say, if that is the case, because we don't know the actual pattern, that you want to recognize, nor do we know your exact requirements. You will need to test that yourself.