The peak LED current of ADPD1080 is 250 mA. How you would suggest to use the device in a compact design powered by a coin battery e.g. CR3032? Such batteries are probably not able to sink such current.
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.