There is actually legit monetary theory about your style of economy: Silvio Gesell 's Freigeld.
(if you can read the German page, it's about 4 times as long and way more in depth). Or rather, Freigeld is an economic philosophy that revolves around your type of money: demurrage currency. It's been tried occasionally (though always in direct competition with other currencies and as a minor part within an otherwise non-demurrage economy) and a lot has been written about it. Ancient Egypt worked with it and a lot of places in higher medieval times (source: surface level Wikipedia reading)
Tl:dr: your money looses value over time so people want to spend it.
But that is likely far too deep for a lighhearted world so at a surface analysis: (more in-theory stuff at the end)
It's a non-issue
Your question reads like the legendary 4chan poster rediscovering agriculture. (reddit link)
What is the difference between growing money and growing stuff you exchange for money? Moneys purpose is to be exchanged for stuff so by growing money directly you're skipping the step of selling it but that's it.
A somewhat minor advantage, easily overcome by the fact that people will initially favour coconut over other crops, driving up their prices (likely to the point where your time spent selling is more than worth it).
Farmland is limited, coconut-suited land even more so. If prices become too high someone will go through the effort of trying to farm the less hospitable areas (closer to the beach, further up the mountain), if they farm coconuts or rice etc.there is irrelevant. You can't simply plant trees everywhere, that's not how plants work. And as explained above, all the other plants will easily compete for growing space economically.
What about catastrophes? If let's say a fire burns down a quarter of the islands coconut trees coconuts of course gain in value. But that doesn't matter. Due to their perishability, the main end use of coconuts is being eaten. So if there's less coconut, their price goes up. Which causes the (relative) price of rice to go down so people eat more rice and less coconut, rebalancing the exchange rates. Similarly, what do non-farmers do with their money? Eat & have a roof over their head. So the prices of their labour will be relative to the competition and amount of resources in the economy. Whether there's more coconut or not in the economy doesn't matter, it's just one good of many, a more efficient barter economy. A really rich person? Feed more livestock. Which is likely to also not yield that significant return because they'll want to eat it themselves and selling a lot means meat is worth less.
Your money having real value and being backed by the real economy will by and large prevent bubbles, in- and deflation outside of changes in actual economic activity (for example industrial progress will "deflate" prices by making stuff cheaper), but within reason. Unless some non-coconut-quasi-currency like stocks, bonds, debt letters etc. are introduced.
Back to Freigeld. If you read through it (in German) you soon realise that the money part of the whole is simply assumed a given without much thought while the consequences thereof (and the required adjustments to them) are given far more thought. One of these is land reform. Due to currency loosing it's value, permanent value stores (and especially generating ones like a plantation) will see incredible price increases which should be countered by land reform as elaborated by Gesell.
One big difference to Gesell's writings however that your currency has innate value (though still depreciating), so instead of investing, you can simply eat that surplus coconut.
