WHAT??? Your lawnmower doesn't have a cup holder? Mine does, and holds my Rolling Rock perfectly, in fact, mine has an ice cooler big enough to hold six Rolling Rocks... Just enough to get the job done 
Alas, only a cup holder. Though before now hadn't considered fab'ing up a cooler to mount on the rear pin.
Truth is, and I know it makes me less of a man to admit this, I wouldn't use the cooler. Yard is only about 2 1/2 acres but when I get started I get in the zone. The yard zone. Every little blade of grass becomes the enemy and all I want to do is kill, kill, kill. Right there on the Group W lawn mower seat; kill, kill, kill. And I don't want to get off the seat until they're all dead. I don't even dismount to move the niece's 14 foot trampoline. Just reach back, grab hold, drive on with the mower and keep cutting the whole time. KILL, KILL, KILL all those little green devils!
(proper citation to Arlo Guthrie)