How much current does the pump require? I assume you mean a pump start relay? It’s rather rare to connect a pump directly to a sprinkler zone as a pump typically needs powerline voltage (110V or 220V). In this situation, you typically use a pump start relay, which has similar electric spec as a standard sprinkler valve (and draws somewhere between 100mA to 200mA current).
In any case, it sounds like what you need to do is not to use a relay board, but rather to increase the current output of your 24VAC transformer. Say, get one that can output 1amp, or even 1.5amp.