Good news! If you have a Japanese PlayStation Network account and a PlayStation 3, that is.
Capcom recently released the PlayStation 2 title Rockman Power Battle Fighters in the Japanese PlayStation Store as a PlayStation 2 Classic. Going for ¥1,234 (about $10.90 USD), this release includes both Rockman: The Power Battle and Rockman 2: The Power Fighters arcade games., along with some extras such as a Versus Mode.
There are a few potential downsides to this, however. First and foremost, this compilation was never released in the west; instead, North America got the two games included in their original forms as a part of the Mega Man Anniversary Collection, which was also a PlayStation 2 release (Europe got zilch as far as any of this goes, as I recall). As such, the odds seem slim that Capcom would release this here.
That means you'll probably need to sign up for a Japanese PlayStation Network account, which is easy enough. However, setting up an acceptable payment option has proven a bit trickier for some, leading them to acquire Japanese PlayStation Network cards from places such as Play-Asia.
If you decide you want to go for it, then here's the link. Just note that if you're signed into another region's PlayStation Network account, the site will try to redirect you and you'll get an error message instead.
Thanks to Vhyper1985 for the tip!