As others have mentioned, you could use that large rock to your advantage, but for less money, you can simply design your house to take advantage of passive cooling methods. Quickly, I'll preface that I get most of these ideas from the visitor center in Zion National Park. It gets exceptionally hot and humid in the summer there, but they maintain near-zero usage of AC due to the building design.
You can position your windows with overhangs or sunshades that passively block sunlight (and potentially some of that rain you mentioned) during the summer months. Indonesia, being so close to the equator (as you said), would likely have less variation in sun angle year round, so it's possible these sunshades would work continuously to prevent heat ingress.
Check out these examples: Zion, Sunshades, Google Images
On a similar note, using Low-E glass can help reduce any stray IR radiation from entering, further helping cool your house.
Passive Cooling Tower
You are making a two-storey building, so you can take advantage of a vertical passive cooling system. I have been next to the one in Zion, and it's amazing how well it works. Check out this diagram.
It works on the principle of evaporative cooling. You have wet fabrics exposed to the air at the top of the tower. Warm air rises from your house through a chimney (of sorts). When it reaches the fabric, the warm air causes some water to evaporate, causing the air to cool as it transfers heat into the water. The cool air then returns down the chimney and into your house.
It's even possible to do this without needing the wet fabrics (though those help significantly due to the latent heat of vaporization of water). Skylights can accomplish the same task, and many have automatic controllers to close when they sense rain.
Ultimately, by having ventilation both high and low, you get passive (or natural) convection cooling. This is also where that large limestone rock can help. If you can get ventilation through that rock, you can take advantage of geothermal buffering, which helps maintain a constant, cooler temperature. Effectively, you are tying the thermal capacitance of your house to the rock, making it harder to heat up easily.