World travelers

Do you're telling me that it had nothing to do with swallows being either European or African?!

It could grip it by the husk.
- It’s not a matter of where it grips it! It’s a matter of weight ratios!
Depends. Does the coconut weigh more than a duck?
- I don't know, I wasn't expecting some kind of Spanish Inquisition.
- Who are you who is so wise in the ways of science?
But then of course, uh, African swallows are non-migratory.

35 million years of coconuts in Asia and they didn't float over until after traders established shipping routes to Asia?

Yes, but for human related reasons. Humans moved them around a lot in Africa and Asia - moving them from Southeast Asia to India and Madagascar is bound to have an impact on the currents they get caught up in.
- are you proposing some kind of Columbus effect where people heading to India will occasionally end up in Taino land by accident
- So thanks to humans more coconuts went for a swim?
According to the first article that popped up in the search results the most likely theory is portugese traders brought them over from madagascar.
Climate change confirmed.

I'm gonna cast doubt on this. It happened too conveniently after people figured out long distance sea travel.

If they would have floated it's much more likely that it happened somewhere in the last million years rather than the last 500.

Not accurate. They were taken by Astronesians during their seaborne migrations.

Read more here

they only think coconuts floated over on their own 500 years ago because austronesians are supernaturally invisible to white people

Bingo. I thought this was interesting and went looking for more information and its fake. They were brought to other parts of the world, first by austronesians and later by European sailors.
- Someone in this thread needs to say who austronesians are
  Edit:
  The Austronesian peoples, sometimes referred to as Austronesian-speaking peoples, are a large group of peoples who have settled in Taiwan, maritime Southeast Asia, parts of mainland Southeast Asia, Micronesia, coastal New Guinea, Island Melanesia, Polynesia, and Madagascar that speak Austronesian languages. They also include indigenous ethnic minorities in Vietnam, Cambodia, Myanmar, Thailand, Hainan, the Comoros, and the Torres Strait Islands. The nations and territories predominantly populated by Austronesian-speaking peoples are sometimes known collectively as Austronesia.
Did austronesians reach the carribean? I thought they made it to madagascar and hawaii, but not the carribean.

No swallows necessary

Caribbean from Asia? did they take the Panama Canal 400 years before it was built? there is not path that isn't crazy

Asia via the Pacific to the Americas, then a swallow grabs one and brings it to the Atlantic coast.
- African, or European?
They went around the horn like a real man!
There's a current originating in Indian ocean flowing south of Africa to the gulf of Mexico, before proceeding north east between Iceland and Great Britain. It's why Scandinavia is so much warmer than the same latitude in the Americas. I'm 55 north in Denmark, and have hardly seen snow this winter, meanwhile Edmonton in Canada is 2° south of that.
Coconuts bobbing around the south of Africa is pretty wild, but not implausible.
- Native Americans and Polynesians Met Around 1200 A.D.
I assumed one finally got lucky and got around the southern tip of Africa while headed west.