What is the maximum current limit of this motor?
Rated Power is given as 220W and Rate voltage is given as 24VDC. According to this maximum current should be 9.166A.


No, a rated unit \$ \neq \$ a maximum unit.

So, if the rated power is 220W and the rated voltage is 24Vdc, then the rated current should be 9.17A.


  But 2.5Amax is also mentioned on the name plate.


By definition the rated current \$ \leq \$ maximum allowed current.  

So, the shown specs are weird.  

Looking up a few other motors from MOTION TECH MOTORS show the same remarkable data:  


EC82M245330ALGB0 MOTOR: 24Vdc 4.5A(max) OUTPUT: 300W RATIO 1:25
EC82L244840ALGBL MOTOR: 24Vdc 4.5A(max) OUTPUT: 400W RATIO 1:32
EC82M244632ALGBL0C MOTOR: 24Vdc 3.0A(max) OUTPUT: 320W RATIO 1:32
EC63L244727ARGBL MOTOR: 24Vdc 3.0A(max) OUTPUT: 270W RATIO 1:25


For all these motors, the output power is more than the (electrical) input power, which is, of course, nonsense. It would make more sense when when the output would be a factor ten less.
But then, motors with the same input voltage and current having a higher RATIO also have a higher output power, which little sense either. A higher reduction ratio would give an equal (same number of gear stages) or lower efficiency (more gear stages).
So, I fail to see any logic here.


  So what should I consider as the maximum current limit so as to design the protection circuit for this motor?  


In the linked datasheet the MOTOR specs show the max current, so, (for what the specs are worth) I'd go for 2.5 A (max).  

But I'd rather recommend using/finding a motor with decent/plausible specs.