The center of gravity and center of mass coincide as long as the gravitational field is uniform (negligible changes from point to point on the object). Under these conditions, for analyzing motion, stability, etc., it is correct to model the gravitational force as acting through the center of mass.
The center of buoyancy and center of volume of a submerged object coincide if, again, the gravitational field doesn't change over the object, and additionally, the density of the fluid does not change appreciably in the region surrounding the object. It is correct under these conditions to model the buoyancy force as acting through the center of volume (the "average" of all the points contained in the object). This center of volume, in general, only coincides with the center of mass if the object is of uniform density. If it is not--has dense areas and light areas--the center of mass and center of buoyancy are not the same, and if you pretend they are, you will reach incorrect conclusions.
As has been pointed out in other answers, neither gravity nor buoyancy actually act at a concentrated point; but for a rigid body all that matters is the integrated force over the entire body.