Piezo barely audible
The problem is not current, but voltage.  Piezo elements are inherently fairly high voltage devices; there are those which will work somewhat at logic levels and may even be designed for it, but they will be louder at higher voltage up to the point where they depolarize (or depending on how mounted, conceivably crack). 

Some of the low voltage piezo alert devices which do not need an external oscillator because they have an internal one exploit resonance behavior to boost the voltage above the external supply.

Additionally, piezo devices will generate more output at higher audio frequencies than lower ones - they can move quickly, but not very far.

While your question says piezeo, and that is what I have answered, that may not actually help your problem.  Your link is to the data sheet for a magnetic transducer with a coil, which is a completely different sort of device.  A piezo is a crystal of a special ceramic which deforms in response to an electric field (typically it is bonded to a metal disc for a better impedance match to air at audio frequency)