What location has the most Cumulus clouds (percentage wise) year round?

Tropic latitudes roughly 30 N to 30 S. Atmosphere is conditionally unstable year round resulting in convection.

The answer above is correct and to the point but, perhaps, it needs a bit of explanation.

Meteorology is about the difference in temperature, pressure and moisture of different air masses. As you know, the temperature sinks with altitude, due to the adiabatic effect of a lesser pressure aloft. But how fast does it sink tells how stable or unstable the air is.

If the measure adiabatic lapse rate (how fast it sinks) is less than that of the wet adiabatic one (0.5 C per 100 m), air that rises quickly cools down to an equal surrounding temperature and stops rising. It may even form an inversion if the air is warmer over colder one.

If it is more than the dry adiabatic lapse rate (1 C per 100 m) the air is unstable; it will never cool down enough and keeps rising to the top of the troposphere. That's what happens when we have thunderstorms.

When it is between the two, it is then called conditionally unstable and the condition is simply; how much moisture there is in the air.

Now, the higher the temperature, the more moisture the air can contain and the tropical region is, of course, the warmest region on earth. But there is more than that: at the tropopause; the separation between the troposphere and the stratosphere, it is much colder between the tropics than at the poles. Strange, isn't it? Well, it is due to the fact that, the air being warmer at ground level, it takes more air for an equal pressure. Add to that, that the earth spins and created a bulge of the atmosphere at the equator, plus that the strong convections brings a lot of air upward, the tropopause is nearly twice as high (up to 18 km) at the equator, than at the poles.

Because of that, between the tropics, the atmosphere works like a big chimney, with much warm and moist air under, and very cold air very high up. It makes the perfect condition to see the air rising, reaching dew point temperature and create the nice cauliflower-like clouds that we call a cumulus.