In operation the average current through each diode will be your load current. But that's average.
In detail... during a cycle each diode must carry a brief pulse which is much higher than your load current. So your diodes really ought to be rated higher than your load current.
Not only that, power-up causes large surges to go through the capacitor because it is like a dead short when it is not charged. So your diodes must endure overcurrent for a few cycles.
You probably can get by with 1A diodes rated for reverse 50V. This is a common 1N4001. Or use a bridge rectifier with the same rating.
If one diode burns up, then you should replace all with 3A rating.