You could use a pressure-sensing pad that in effect "weighed" your coffee jar. If the weight was between "empty" and "just enough left" then it would send a message over the net. You would discount very low weights (jar removed in use) and you would want to average for a few minutes before deciding in order avoid artifacts when the jar is moved.
It would require that you always returned the jar to the same spot and didn't stack stuff on top of it!
You would need an ethernet or wifi enabled arduino and a suitable (piezo?) pressure sensor.
There may be better ways but that initially springs to mind.