Airbnb-like sites for long term stay

You will probably have to pay a minimum of $10 per day for accommodation using any booking sites like AirBnB.

One option would be to look on the site: https://www.workaway.info/

And see if you can come up with some sort of deal.

The only way you will find somewhere really cheap is by first going somewhere and then trying to find a place to stay with a local. I wouldn't have thought this would be too hard and you will probably be able to find some places for next to nothing. I stayed in Zajecar, Serbia for 80 days, in a house arranged by a Serbian friend, that was usually rented out to students, but was vacant in the summer. It was £50 / month, including electric, which is about 70 EUR/USD. I had serious internet problems though, which was an issue, as like you I work remotely. However, you can get cheap 3G. Given that unemployment is about 17-18% and the the minimum wage, after tax, is about $1/hour, I wouldn't have thought it would be too difficult to find a place if you want to offer something like $100, or maybe even $50, for something in an apartment.

The best places to try and look for a place like this would be places that are not popular with tourists, as I found that they are very curious when an outsider comes. I would recommend Pirot, in the south-east, when I was there, I was asked lots of questions (in Serbian and English) in almost every shop I went to and even in the street. One even offered me a place to stay.

If you really want to chance it, go to a small village and offer something like $50-100 / month to people there. I'm pretty sure you will find somewhere, as many people in the villages live off a very small income from selling vegetables in the summer-autumn.

This all, of course, becomes difficult if you cannot speak Serbian.