Yeah, I've always thought you should go there and try learning it. Second best might be finding some people online that could teach it to you or trying your hand at writing on their Wikipedia.
Since it's relatively easy compared to Spanish, shouldn't you be able to figure out the grammar as you go by checking out the online newspapers and taking comments from people that live there? Maybe you could start a Papiamentu grammar and language source wiki at
and with enough effort you could make the first complete Papiamentu course online strictly through your own experiences.
I've seen a lot of Papiamentu videos on YouTube too and I bet some people from there would be willing to transcribe the speech since that's usually the best way to learn a language and they should be interested in promoting it.
I'd put some work into that too if you started a wiki on the language.