Making his phone ring while the boss is nearby is a cute idea, although it may not garner the desired response (ie: changing his ringtone.) His boss may not care enough to say anything, or he might just apologize quietly and not do anything else. It could also backfire on you if your coworker can trace the incoming call back to you, so tread carefully.
A coworker has a song as their phone's ringtone, and the song lyrics could be flagged NSFW. It does not contain actual cursing, but has tons of obvious sexual innuendo. I think it is disturbing.
If a human being were to speak the lyrics to another human being in the office, would it reasonably be considered sexual harassment? Harassment in the workplace can take many forms, and women are not the only ones allowed to complain about it.
You could take a transcript of the lyrics to HR and ask them what the company's policy is regarding language like this in the office. Not naming the coworker specifically, or even admitting it's someone's ringtone. Just tell them you're trying to gauge what is or is not appropriate around the office. That could help to inform you on what should be done next as well as how likely you are to get support from people outside your department.
Filing a (politely worded) complaint with HR is not necessarily over-reacting. You could even submit the complaint anonymously if you're really worried about it, so they know what's happening without knowing who exactly brought it up.