Traveling on Rhine and Danube rivers.

From Budapest to Belgrade you can travel only on Danube River. Besides overnight cruise ships there are some hydrofoils (if all the way to Belgrade I am not sure) and shorter day cruises. Put this question under Hungary and I am sure James can answer it.

You could do it by bike.

More than one ferry company operates on the Rhine in Germany, in addition to the K-D Line that Rick mentions in his Germany book.

Regarding Danube routes such as Vienna-Budapest that are served by ferry, Rick suggest that they are "less scenic and romantic than you might imagine." See. p. 209 of his Vienna/Austria book or look for Twin City Liner or LOD to Bratislava or Mahart to Budapest (runs in cooperation with DDSG).

A direct train from Budapest to Belgrad takes 8 hours, either by day or overnight.

Thanks for the info it's very encouraging to have your help. Now Emily you are an optimist I can tell! I actually COULD do it by bike it occurs to me. My husband would be reluctant since he " knows me" but I'm at an age where it's either do it or never do it. Hmmm. Emily, have you made this trip by bike? I am a 54 year old woman that has sort of been letting herself go. My husband will probably insist I ride a bike somewhere here first. Tell me about your bike ride if you have time.
Warm regards
Tracy

Tracy, I haven't done this by bike, but know that it is possible. Maybe even nice to do just some segments and couple it with short train rides. I did a quick Google and found many blogs and itineraries from folks who have done this.

Getting back to your original question, it is hard to find anything but cruises on the Danube. Some ferries exist (like Vienna to Bratislava), but these are also expensive and probably not what you are looking for.

Thank you for the research! I'm going to have to pay all this great travel advise forward after my trip!

I'll let you know if I end up on a bike for part of this trip!