Now, most Vocaloid's these days do have their own songs, and to avoid copyright in any way, it may help to make them yourself. Now Vocaloid is a japanese program, but there are plenty english ones out there, i'm suggesting if you want your character to have their own song to download a free version or a trial to see how you go, now I know by experience that these programs usually do not work on laptops, so it's best to download on compters. If you don't like the pitch with the finished product, it's best to find a voice close to the one your character has, use it, then go to audidacity after downloading and pitch it up and down depending on your characters voice. An english vocaloid song example is:
MMD (Miku Miku Dance) Is more or less an anime 3D software where you can create your own character, make them dance to songs and pretty much put a full coregraphy to it, thats about all I have to say, but you can find it for free online, and is best downloaded on computer.
If you're thinking of downloading the programs, its best to see reviews and tutorials for it, reccomend download links below if you want, also, sorry most of it is just Miku, heh~!
