Defining power supply current specification
Start with the dropout voltage for the relay.  This is the minimum voltage that will hold in the relay armature.  Let's assume that it is 38 V for a nominal 48 V relay.  That is a delta of 10 V, the amount of decrease in the capacitor voltage over 30 ms.  You can use the equation for the exponential voltage decrease in an R-C circuit, with 300 ohms for R, to calculate C.

A shortcut is to use the constant-current equation as a first-order approximation:

E C = i t

E = voltage change during time t

C is the capacitor size in farads

i is a constant discharge current

t is the discharge time

For i, use Ohm's Law to calculate the coil current at 48 V and 38 V, and take the average.  Use this to calculate C.  I get 430 uF; 470 uF gets you a little margin, and 1000 uF is much better if you can handle the size.  For long term reliability, use parts overrated by 100%: for a 48 V circuit, use 100 V capacitors, diodes, etc.