What capacitor needs to be used for a circuit that limits the current?
I did not get context of having limited current of \$2.7\, \mathrm{mA}\$. however, regarding the capacitor:  

The capacitor recommended value is \$ 4.7\, \mathrm{uF}\$. Other than that, voltage rating of the capacitor should be more than the expected input voltage. Since, the IC input voltage is rated upto \$42\, \mathrm{V}\$, a \$50\, \mathrm{V}\$ capacitor has been recommeded.  




  Input Capacitor:
  In order to reduce input ripple, mount ceramic capacitor of low ESR near the VCCpin. In  the  BD9G101G,  it  is 
  recommended  the  4.7μF  or  more  capacitorvalue.  In  case  of 
  using  the  electrolytic  capacitor, mount about 1μF ceramic capacitor
  in parallel in order to prevent oscillation  



go for Ceramic capacitor if cost is not the issue  
The current limitation at the input side may demand bigger capacitor (depending on the load)




Edit 2: since the input current is limited, the BD9G101G might not achieve a good load regulation (responding as fast as possible to the changing load). If you have the estimate of peak current demand form the load of BD9G101G,then you can estimate the required value of the capacitor so that, the main circuit will not be burdened. The capacitors will slowly charge back to normal voltage via the limited current path.