For example, in my country, the price of coconuts steadily rises, despite the fact that we still have plenty of coconuts. The same with vegetables.
Is this caused primarily by an increase in the cost of labor as a factor input, or are other forces at play?
Real prices are fundamentally determined by supply, demand, and the market structure.
As you say, it cannot be a supply effect, as the supply of, say, coconuts, appears to be constant to you.
It could be an increase in nominal prices at the rate of inflation. In that case, prices for some goods just become more expensive because the relative supply of money is growing, real prices do not change.
Alternatively, you could be facing more international demand for your goods. If international demand for coconuts goes up, exports and local demand have to "fight" for the supply of coconuts, leading to an increase in prices.
To make it simple: let say your coconuts production is constant over time but the population is growing. It's a constant supply but an increasing demand, resulting in an increase of coconuts price.
If the prices were constant, the demand would be higher and thus not fully satisfied.
