Oh, if only there were such a thing as "standard practice" when renting as a foreigner.
Go to Google, type in "U.S. dollar to Argentine peso" and show your landlord what comes up on the screen. I've never had a landlord argue with what Google shows. Currently, it's this:
1 U.S. dollar = 4.20450723 Argentine pesos
This "non official" rate business is sketchy as hell, and something tells me it will go up every month. You could suggest setting a set peso amount to pay each month. That's what I did, but I imagine a lot of landlords/realtors wouldn't go for it. Or, offer to pay the exact exchange rate as it is each month on the day you pay rent. So if you pay today, it would be X dollars x 4.204blahblah pesos. Maybe next month it will be X dollars x 4.3567blahblah pesos.
You never can tell how they'll react to this type of stuff, but hopefully she will agree to one of these options. Getting whatever agreement you come to in writing with both of your signatures won't hurt. Hope this helps.