ADPD1080 work from CR3032 battery

Assuming the LED duty cycle is low  , i.e.  the LED on time  is very much smaller that the LED off  time  , then a similar technique to that used in Infra Red   Remote control units for a TV   can be used .

The technique  involves  connecting a  low ESR capacitor of  usually    somewhere between  4.7uF and   10 uF    between   the LED supply and the LED   ground return . It should be easy to establish the actual value required   using an  oscilloscope. What you are looking for is minimal pulse "droop".
An example of this  is shown in  Fig  36 on page  #31 of the datasheet .
One capacitor can be used for  all three LED's   or an individual capacitor for each LED , sizing  the actual value ('s)  appropriately of course.

It works  like this  :- While the LED's are off the capacitor, is charging  up to  the LED supply voltage . When the LED is turned on the capacitor is  providing the peak current required and not the coin cell. When the LED is off the cycle repeats.  

Assuming the LED duty cycle is low  , i.e.  the LED on time  is very much smaller that the LED off  time  , then a similar technique to that used in Infra Red   Remote control units for a TV   can be used .

The technique  involves  connecting a  low ESR capacitor of  usually    somewhere between  4.7uF and   10 uF    between   the LED supply and the LED   ground return . It should be easy to establish the actual value required   using an  oscilloscope. What you are looking for is minimal pulse "droop".
An example of this  is shown in  Fig  36 on page  #31 of the datasheet .
One capacitor can be used for  all three LED's   or an individual capacitor for each LED , sizing  the actual value ('s)  appropriately of course.

It works  like this  :- While the LED's are off the capacitor, is charging  up to  the LED supply voltage . When the LED is turned on the capacitor is  providing the peak current required and not the coin cell. When the LED is off the cycle repeats.