If you google earth Buenos Aires...northern side.. you will see SO MUCH ORANGE from all the clay courts there are in the city. I don't think you will have any trouble finding any. They are EVERYWHERE.
but it depends where you live...
I only know Olivos (there is one 2 blocks from the Borges RR station)
and Belgrano (Belgrano Athletic Club) where my cousin plays.
I emailed the BAC before I arrived in BA to ask if I could have a temporary membership... no special offers but I am going to tag along with my cousin next time she plays and see what's up.
There is a place called Club Puente Tenis - it's on niceto vega between juan b justo y humboldt. It's small - only three clay courts - and one of them is covered. I think it's 63 pesos an hour.