The area adjacent to Lake Erie in Cleveland is called the North Coast. Head east towards Buffalo, and there it’s called the South Shore.
Non sequitur. What I said was that discussions such as this is just another case of futile hairsplitting (at least is what I meant).
I see. Anyway, the general usage I’m familiar with is that there are oceans and there are seas and the extent of an ocean is not restricted by the extent of a sea. In other words, the Atlantic Ocean includes the Adriatic, Aegean, Balearic, Baltic, Black, Carribbean, Celtic, Ionian, Irish, Ligurian, Marmara, Mediterranean, North, Norwegian, Sargasso, Scotia, and Tyrrhenian seas, the Bay of Biscay, the gulfs of Bothnia, Finland, Guinea, Mexico, and St. Lawrence, the English Channel, and so on. Atlantic Ocean. Indian Ocean. Pacific Ocean.
I would imagine that they’d try to avoid the No True Scotsman’s fallacy as well. 
As a Michigander, I’ve never heard the Lake Michigan shoreline refered to as “the third coast.”
I have heard it called, “the middle coast.” I guess that makes me a wierdo.
If you’re determined to settle this with Google, why not do a Googlefight?
third coast Texas vs third coast Michigan
The problem is, there is also:
third coast Gulf of Mexico vs third coast Great Lakes
Anyone think of a good tie-breaker?
I do have some background in Geography, but I’m just short of a minor degree in that field.
I view the word “coast” as land meeting the ocean at sea-level (0 feet/meters in elevation). Lakes don’t have coasts, they have “shores”. Rivers have “banks”.
Land surrounding seas seems trickier to me…“Sea coast” and “sea shore” is used almost equally, but I view the word “sea” as a body of water at or below 0 feet/meters in elevation…hence, Mediterranean Sea (which has it’s own basin even though the Strait of Gibraltar exists between it and the Atlantic), Salton Sea, Dead Sea, Caspian Sea…but there are probably exceptions, albeit few (ex.- salinity and/or cultural/ancient reasons…Aral Sea is above sea-level, but it’s saline.)
Therefore, the Great Lakes having elevations in hundreds of feet above sea-level are aptly named lakes, therefore they do not have coasts, they have shores. The St. Lawrence River (Seaway) has banks until it reaches sea-level, then it becomes the gulf of St. Lawrence (which is then part of the Atlantic Ocean).
The gulf states do have a coast by inclusion of the Atlantic, just like the Gulf of California by inclusion of the Pacific, but nonetheless, the gulfs are just an extension of the oceans itself, just like the St. Lawrence gulf is to the Atlantic. So the gulf states really can’t claim a third coast either although they can be considered “The South Coast” in relation to the rest of the States. But, the Great Lake States can’t claim “The North Coast” designation. “The North/South/East/West Shores” would probably be a poor choice too, since it really talks more about which side of 5 major lakes people live on, which would be pretty confusing for most.
Bibliophage is right in assigning Alaska with “third coast” honors which meshes with the Artic Ocean.
Canada also has three coasts, but not a fourth by using the Great lakes as their “South Coast”.
But if the case is closed, how do you get the beer bottles out? 
Despite the history of the country and its economic development, I think the first coast would have to be the West Coast. After all, it’s often called simply “the coast!”