Yup, decided to do another one - mostly because it was interesting and this one <b>definitely</b> wasn't going to be available in app form.
As before with my other downloader, this particular script relies on the free 'iDownloads PLUS - Download Manager!' app in the app store (though it can be retooled to use other downloaders, provided they have a custom URL for launching the download URL in the app). I just happen to like this one because it's free and offers background downloads and 'Open In' functionality to move files afterwards.
Usage is with the bookmark listed at the bottom of the gist.
Visit a page in Safari on Soundcloud (m.soundcloud.com) on your iOS device, find one with a song you like, then click on the bookmark to trigger a download of the .mp3 (even if the page does not offer a direct download link itself).
Unfortunately the limitations of iOS make it so that .mp3 files you download can't be added to your device's music library programmatically. You'll have to save the .mp3 file from your device to iTunes and then sync it back to your device (or have a separate music player app, of which there are many, that you can 'Open In' the .mp3 file). In the meantime, iDownloads also offers a built-in media player so you can get to the listening :)
<strike>There's an issue at the moment where the script takes a long delay in attempting to get a client id for the download. I'm not quite sure why it's doing that. When I was testing the script on my MBP, I didn't experience delays even remotely similar. I'll work on that more later when I get a chance and hopefully eliminate the delay.</strike>