Sure they would (as I guess you later realized when you took back this statement). Namely, by hypothesizing that the sun revolves around the earth in an orbit that’s tilted with respect to the earth’s axis. In the same way that we now explain the seasons by saying that the earth revolves around the sun in an orbit that’s tilted with respect to the earth’s axis.
It’s the tilt itself that’s the important feature for causing the seasons, not which body is actually doing the revolving. Works either way. (And in fact, that’s how seasons were explained by geocentric astronomers for millennia before the heliocentric hypothesis gained currency. What, you think Ptolemy and his ilk just didn’t notice that seasons changed annually, or didn’t bother trying to account for it? ;))
AFAIK, you can’t demonstrate heliocentrism just by appeals to observational astronomy (changing seasons, etc.) in the same way that you can demonstrate the earth’s sphericity by appealing to observation of things like ships on the horizon, the shape of the earth’s shadow during lunar eclipses, etc.
The earth and the sun are revolving about a common center of gravity, and the appearance of that motion changes depending on where you are in the system. You can’t tell just from celestial kinematic phenomena (i.e., the geometrical appearance of the relative motion of earth and sun) that the common center of gravity is inside the sun instead of inside the earth.
To make that case, you need celestial dynamics, i.e., Newtonian theory of force and gravity based on the concept of mass. Small masses orbit large masses, not vice versa. If you can get a geocentrist to accept Newtonian dynamics, and to agree that the sun is much more massive than the earth, and to agree that the other planets do orbit the sun instead of the earth (which is something that you can use kinematic arguments for), then you’ve got a strong case for heliocentrism.
As a historian of astronomy and mathematics (although not a specialist in the early modern European period), I’ve seen a lot of the historical arguments for and against heliocentrism, and ISTM that the modern geocentrist movement has nothing new. What clinched the argument for heliocentrism back in the seventeenth and eighteenth centuries was Newtonian dynamics. You simply can’t make sense of basic physics if you’re going to argue that the sun can be far more massive than the earth but at the same time orbit the earth. (And if you try to argue that the sun is smaller than the earth, that’ll get you into other problems.)