I need to use a coin cell battery as a source for supplying 3.0 V at about 70-80 mA for about 2 hr per day. The coin cell battery I want to use, its spec sheet doesn't tell me much about what I want to get out of it. Here is the data sheet link: http://data.energizer.com/PDFs/cr2320.pdf. 80 mA seems a lot for me for this little coin cell batteries as they are only used for very low power electronics but I am not quite sure if it could be applicable to my case as the data sheet is not very clear to me.
Read the datasheet. It tells you what you need to know. I could go into details, but that would be pointless as the datasheet already is doing a nice job. You're complaint that it "doesn't tell me much" only shows you didn't really read it.
In particular, note the rated capacity of 135 mAh. Even if the battery could deliver 70 mA and still maintain that capacity, how long would it last? This is very simple arthimetic. 135 mAh / 70 mA = 1.9 h. So it wouldn't even last for one of your 2 hour sessions.
However, 70 mA is waaaaay past any reasonable operating point for this battery, as the datasheet again makes quite clear. Note that all the capacity ratings are with 10 kΩ (290 µA) load, and that 600 Ω (6.8 mA) is considered a "pulsed" load.
As is too often the case here, the answer is READ THE DATASHEET.
The CR2032 has a lot of internal resistance. I would expect the short circuit current to be in the 80mA range or less, and that perhaps for not very long (due to polarization effects).
Using 6.9mA pulse test on the datasheet the graph indicates a 25-30\$\Omega\$ internal resistance, which would give you ~100mA short circuit current, so at 80mA you'd be down to half a volt or so.