I don't know of any midi players for mobile, but there are quite a few music players with adjustable speed for normal music files (wav, mp3, etc). They've come a long way over the last 15 years, and the sound quality on many of them is excellent. If you slow them down too much (say, to 50%), it would sound ridiculous, but then even a midi file would sound wrong when modified to that extent. However, if you're staying within the standard +/-15%, you can't go wrong with any of these:

Tempo Magic / Tempo Magic Pro
Tempo Slow
djay

There are others still, but these are the best I've found for ballroom dancers. I'm sorry I don't have links -- you'll have to search on the name in the iOS App Store / Google Marketplace. Also, I know these are available for iOS, but I don't know which, if any, are also available for Android. Maybe some of our Android fans can let us know.

Regards,
Jonathan Atkinson
www.ballroomdancers.com