I'm pretty sure Brazil would be delighted to receive a regular check from the rest of the world in exchange for defending part of the rainforest. As long as they get their cut, they're going to be happy. Just make the payments conditional on the continued protection of the forest; otherwise they can be expected to renege eventually.
This is exactly what it means to "buy property," by the way: nobody else can use it and the government enforces that if necessary using men with guns. So what I'm suggesting is only a slight refinement of the normal and expected arrangement when buying property.
Buying property is a one-time deal, not a "regular check". Also this is between nations so a purchase of land means transferring sovereignty as well.
It seems what you're talking about is leasing the land, which is entirely different. Also unlikely considering how much industry it would displace in their economy (which is the reason this is a problem in the first place).
So no land rights, just paying them to maintain a rainforest? That has nothing to do with (buying) property at all.
That kind of deal would have ridiculous rates for the opportunity cost, won't stop illegal deforestation or crimes through plausible deniability, and we'll still end up with an expensive military and political presence to oversee everything. Also many other countries will start to ransom environmental support for a paycheck.
I see nothing but negatives with this strategy. We can't just pay countries to change their behavior that easily.
there is no way that this payment arrangement is stable over the long term (more than 10 years).
The only thing that will happen is the locals will become resentful of the foreigners who are preventing them from using their own land, someone will rise to power riding on that resentment, they'll use the money to raise an army, and then they'll kick out the foreigners and renege on the deal.
there is no such things as "buying property" between nations with out transferring sovereignty. Look at the louisiana purchase, purchase of alaska, etc for examples of doing it correctly in a long term sustainable way.
look at hong kong for examples of doing it wrong: the chinese "bought" hong kong from the british 100+ years ago but guess what? the hong kong people don't care.
All things considered, the arrangement of Guantanamo Bay, where Cuba retained sovereignty and gave the US an indefinite lease, which survived Cold War hostilities, even the missile crisis, without disruption by anti-US sentiment, has been relatively stable.
Additional resources will allow to purchase equipment, pave roads (like the BR-319 that article is describing). And in a decade the deforestation will only increase. An instability or crisis will likely have the opposite effect. In particular, road surface degradation or disruptions in the exports.
This is exactly what it means to "buy property," by the way: nobody else can use it and the government enforces that if necessary using men with guns. So what I'm suggesting is only a slight refinement of the normal and expected arrangement when buying property.