Is there any easy way to estimate the size of a central air unit for my home?

Not really, whithout a good inspection. Yes, there are rules of thumb for tonage vs. square footage but they can't address important issues like the length of runs you have and whether the right sized unit would be compatible with your current furnace.

There are lots of "how to buy and choose" a central air unit out there:
http://www.google.com/search?num=100&hl=en&lr=&newwindow=1&q=central+air+size&btnG=Search

... but your best info will come from someone inspecting your current system, house size, floorplan, efficiency of windows, etc...

Hope this helps a little.

In the Ohio and areas around Ohio 600 square foot per ton= 12,000 BTU. This can change because of windows especially south facing windows and insulation value ETC.