Maximum discharge rate of coin cell batteries
The maximum discharge rate is basically limited by the internal serial resistance of the battery and the heat generated through it.

It will vary depending the chemistry, packaging and so forth.

Usually these values will be given by the manufacturer.

However, you need to be careful not to draw more amps than the manufacturer specification if you don't want to get some nice fire.

Usually the discharge rate is given in x/C in which C is the capacity in mAh. 

For example a 2200mAh battery with a discharge capacity of 2C means you can draw 4400mA, 0.5C would be 1100mA.

This is also given for the charging rate.