It is too short for a long term indefinite contract on an apartment.
Granadainfo has some places with good prices for long stays.
Carmen's Apartment would be a good choice and the price per night is around 25 euros for low-season long stays:
https://granadainfo.com/ca/Another possibility would be Casa San Pedro which also costs about 25 euros for long stays in the low season:
https://granadainfo.com/sp/Very close to Casa San Pedro is the Spanish School "Carmen de las Cuevas".
There's more information here:
https://en.carmencuevas.com/They also organise guitar and flamenco classes.
It is always a good idea to ask the owners of apartments to give you a discount for long stays at low season.