Granite ‘floats’ because it is a ‘sial’ rock. That means its composition is predominantly Si (silicate minerals) and Al (aluminium minerals). It is lighter than the ‘sima’ rocks of oceanic crust (mainly magnesium silicate minerals). Sial is less dense than sima, since it contains less iron and less magnesium, and more aluminium.
The bulk of the continents are going to be igneous rocks (like granite and basalt), since they form first, and are what the proto-continents are made of. You can’t have a sedimentary rock unless there is a pre-existing rock to break down. You can’t have a metamorphic rock unless there is a pre-existing rock to subject to a new heat and/or temperature regime.
So if you identify an igneous rock which is tougher than granite for your planet, you need to (a) find out its main chemical composition and density, then (b) alter the chemical composition of your sima so that your new rock still ‘floats’ on it. This is what Sarriesfan’s answer proposes, I think. I don’t know enough about the toughness of basalt to say how it compares to granite.
Meanwhile... erosion and weathering (IIRC ‘weathering’ is breaking the rock up, and ‘erosion’ is moving the broken bits to somewhere else).
Granite consists of the minerals quartz, feldspar and mica (biotite, muscovite and/or amphibole). Here’s what happens to those minerals when they are weathered. Quartz and muscovite mica are (usually) most resistant to weathering because they are physically tougher. Here’s some pictures of the stages of weathering in granite.
In warmer climates like the tropics, chemical weathering (chemical breakdown) predominates. This is because the speed of chemical reactions roughly doubles for every 10 degrees C increase in temperature. This paper lists how various types of rocks respond to chemical weathering. Chemical weathering includes being dissolved in water, so a wet climate will have faster chemical weathering than a dry climate.
- Toughest = granite. Comes equal first with gneiss & mica schist
- Gabbro and sandstone
- Volcanic rocks
- Serpentine and amphibolite
- Carbonate rocks (12 times more prone to chemical erosion than granite). Chalk, limestone, marble.
- Rock salt (80 times more prone to chemical erosion than granite)
In temperate and arctic climates physical weathering (frost shattering and so on) become more important in destroying rocks. Basically, things which spring to mind when a layman thinks of erosion – battering by waves, being fractured by ice crystals or scoured away by the wind – are the main way that rocks are broken down in cold and temperate places. Chemical weathering still happens, but at a much slower pace.
In very cold climates, quartz isn’t so tough! Here is a paper on cryogenic weathering of granite in Antarctica. The quartz is being fractured preferentially over other minerals because of the low temperature.
So if your planet is amazingly cold, other rocks may last longer than granite, since its quartz is taking a hammering and the chemical reactions which destroy carbonates (like the marble which nigel222 suggested) will be very slow. It won't be very hospitable to human life, however!