Choosing the right capacitor
The ER341245 data sheet says it can supply 450mA continuous, and 1000mA pulse. 

So it does not look like a capacitor is needed to protect it from damage by a 60mA peak.

According to the data sheet the battery capacity is quite sensitive to the discharge rate, so trying to smooth out the discharge rate might have some benefit.

"peak last 25ms and its frequency is 16Hz"

So every 62.5ms, there is a 25ms peak.

The average current appears to be 38mA (25ms * 60mA + 37.5ms * 20mA)

The peak seems to be too large a fraction of the time, and not much bigger than the normal current flow to make a lot of difference. 

I would have to do some experiments to discover how much, if any, improvement a capacitor used to smooth out the peak would have on that batteries capacity.

Put another way, the batteries 'standard' discharge is 2mA, and it falls from 36Ah to 25Ah, about 1/3rd, by increasing the discharge rate by a factor of 50. (50x faster discharge, 1/3rd less capacity)

A 'perfectly smooth' discharge rate would be 38mA, which is about 2/3rd of the peak 60mA, so any improvement in capacity might be hard to detect.