There are a lot of local deals from JAL and ANA which change often. These are put up on their mileage program campaign pages which are unfortunately in Japanese only. If there's interest I can put up some updates here every now and then, but for the meantime, these two are noteworthy I think:

From JAL:
http://www.jal.co.jp/121campaign/flyon/

From ANA:
http://www.ana.co.jp/amc/news/cpn_premipoint/

In a nutshell, if you register for these campaigns you can earn 1,360 fly-on / premium points on 100% earning fares, and 1,220 fly-on / premium points on 75% earning fares for flights between Tokyo and Osaka. They have already been ongoing for a couple of months now but last until Dec.31 of this year.

These may be probably provide the closest equivalent to what could be a mileage run for those based in Japan, land of the sky-high ticket prices and fuel surcharges.