Question about "Upgrading" within Coach
 

I was wondering if any airline allows you to use miles to upgrade to "premium economy" or "extra legroom" seating within the coach cabin.

Several international airlines do. For one, British Airways does, and I believe AA miles or BA Avios can be used to do this.

Premium Economy is (by generally accepted definition) not in the same cabin as coach seats; extra legroom typically is.

The only airline I know of that allows points to be used to upgrade to extra legroom is JetBlue and that only works for members of the TrueBlue program who have Mosaic status. For the other airlines I'm familiar with extra legroom is a cash transaction or an elite status benefit but not a cash proposition.

For Premium Economy upgrade options are more common, though not 100% universal. Expect to pay the fare difference for that upgrade in advance of the day of departure; on the day of travel the cash option may be at a discounted, fixed rate. Points upgrades are a known entity on airlines with a longer-operating premium economy product (e.g. BA as mentioned above) and not always an option in newer programs. There also are likely to be fare restrictions on getting those upgrades; Lufthansa only allows W and higher economy fares to upgrade into Premium Economy, for example.