NRF24L01 Connection Not Working
I was just researching the exact question and I have some bad news.

The ORIGINAL nrf24l01+ alone use around 10-12 ma in transmitting, but unoriginal might even draw more. (https://www.sparkfun.com/datasheets/Components/SMD/nRF24L01Pluss_Preliminary_Product_Specification_v1_0.pdf)

Nevertheless a standard CR2032 battery is simply not made to supply more than a few milliamps at the best, leaving your nrf24L01+ lacking enough current.

There is something called shockburst which can lower your consumption considerably at the cost of range - but if it will succeed in transmitting with one CR2032 I'm not sure about. 

Edit:
If you add a capacitor you need to cover at least a 10ma drain for around 15ms (turn on - send - turn of immediately), that will require a minimum of a 200µF capacitor at 3V to be able to deliver the current while keeping above 2.0v.