Sure! Not easy but doable. I don't know why everyone is so keen living in Palermo, you can find so much cheaper places in equally nice, safe (if not even safer?) yet more Argentinian barrios like zona norte (Martínez, San Isidro..) look for FB groups like "alquiler / vender dueno directo" and strolling around the streets of the barrio you would like to live in and look for ads at supermarkets etc. saying "alquiler" Good luck!