I did this about 20 years ago when I'd just started as an apprentice. I got hold of an evaporative air cooler, the type that you fill with water or ice, gutted it & fitted a domestic fridge compressor, wound quarter tube inside a tube with a small fan on the end for the condenser with a hose that ran outside to exhaust the warm air & fitted a small evaportor in front of the existing cooler fan. It didn't work. As Peter said the compressor, condenser etc. need to to be sized for the job. A domestic fridge compressor is way too small.
The only other way I can think of doing it using a domestic fridge compressor is to cool a large amount of water overnight (do you get cheaper overnight electricity where you are?) & then circulate that cooled water through some sort of heat exchanger with a fan during the day.