Powering an Arduino Mini Pro using a CR2032 battery as a remote control
You should take a look at ATmega328P datasheet


  On page 2, it says: Six Sleep Modes: Idle, ADC Noise Reduction, Power-save, Power-down, Standby, and Extended Standby


These are the modes which can be used to put Arduino Pro Mini in stand-by. You can search for them at datasheet and choose the only that better applies to you. To learn more about sleep mode and other methods to save battery, you can take a look at this source: Arduino Low Power - How To Run ATmega328P For a Year On Coin Cell Battery 

On the datasheet of battery, you should pay attention at its charge: 


  Typical Capacity: 240 mAh (to 2.0 volts)


This means that from 3 to 2 Volts, it relases 240 mAh. This is the charge you can expect to use. Using the consumptions rates you posted above

NRF24L01: 10 mA per second (low-ball)
ATmega328P: 5 mA per second (low-ball)
CR2032: 240 mAh
Time: 240mAh/(10mA + 5mA) = 16 hours


Which is not so much. To increase this autonomy, the link I posted above is quite useful because it will show you alternatives like removing the voltage regulator that will reduce drastically your consumption. Now, if you feel really adventurous, you may take a look at how to underclock your board: Arduino pro mini @ 1MHz - 1.8V. This is a very efficient way to save power where clock frequency is not a must.



EDIT after comments:

The 16 hours were computed using 5mA for the Arduino (which is a value for power consumption that can be expected on active mode) and 10mA for the NRF24L01. You have to estimate a sleep mode consumption for both and a percentage of time in sleep mode if you want to estimate an autonomy. At the link I sent you about sleep mode there are some tables with power consumption in different configurations.

ATmega328P can run with a minumum of 1.8 Volts, while nRF24L01+ can while with a minimum of 1.9V - see datasheet. So probably you are going to have a little bit more than 240mAh to work with. Your battery won't have 3v all the time. It is going to start with 3V (maybe a litte bit more) and gradually reduces it voltage as the charge is provided to the circuit. Once the voltage goes bellow 1.9V, nRF24L01+ won't be guaranteed to work properly.

Definitely, to sleep the Pro Mini, just waking it up when using, is the right way to design this circuit. According to this reference I posted above, power consumption for Arduino should be 0.90 mA. At the item 5.1 of nRF24L01+ datasheet, it is described that it consumes 0.32mA at standby mode II. If you sleep the Pro Mini for, let's say, 90% of the time, without removing leds or voltage regulators, you can estimate that

t = 240mAh * (0.1/(5mA+10mA) + (0.9/(0.9mA+0.32mA)) = 178.65 hours


If you use strategies to reduce Arduino power consumption, like the ones I send you above, you can increase this time. You will also save power if you change nRF24L01+ from standby mode 2 to standby mode 1. Check the database to see which one fit your needs.