Snap! My DS, 17mths, is also a bit of a whinger, that is, unless, he is constantly entertained. To be honest, I prefer the playing, entertaining, constantly being on my feet, to the whining so this is how I cope.
Keep changing the scenery- garden, upstairs, bit of TV, park, visit people, baby group etc.
The whinging around the supermarket, which I cannot avoid because I take my 80yr old nan food shopping, completely halted on the most recent trip on production of a lollipop. I have resisted this kind of junk for 17mths but, other than the sticky hands, hair, face and trolley, I actually found the shopping trip quite pleasant. I brushed his teeth when I got back!
Gradually though, as DS is getting older, he is getting easier and I have to say I never thought I had this much patience and sometimes, I am actually quite proud of myself for not losing it completely.