Just a few clarifications: a) it is legal in Argentina to sign a contract in any foreign currency; b) if the contracts states the price in a foreign currency, the creditor may refuse payment in any other currency; c) the creditor may also refuse to accept partial payments; d) whatever the contracts states is very important to establish if you have any legal way of paying in pesos.
The best advise is always to negotiate with the landlord. Good tenants are difficult to find and, as someone said before, your landlord could always go and buy dollars with the pesos you give him/her.
Good luck!