In solids, is it phonons, or is it the oscillations of electrons in bands, that emit most of the blackbody radiation? In solids (most any object we see), which tends to emit most of the blackbody radiation: phonons (atomic, or molecular dipole, lattice vibrations) or oscillating electrons in their energy bands? 
 A: A couple snippets from the web:
I can't find the actual document name, but it's here

Phonons are quantized lattice vibrations. They possess small energies
  (up to approximately 100meV) and a momentum of the order of that of an
  electron in a semiconductor. 
  Which suggests that phonon energy is far too small to emit photons (other than longwave radio, perhaps).

The wikipedia article on direct vs indirect bandgap material says that phonons are only involved in emission or absorption when the photon's energy is slightly greater than that involved in an electron transition, so the photon "makes up the difference." 
But keep in mind that there is no physical phonon particle: it's just a way of describing the quantized vibrational energy in a solid.  You can't directly convert vibrational energy into a photon, although the energy can affect the final energy of a photon emitted in a quantum process (such as electron level shifts).   There's a pretty good discussion at this Physics.SE  page.
A: Excellent question. The excitations involved are from occupied conduction (metals) or valence states (insulators, semiconductors) to unoccupied conduction band states. These form a continuum so can emit a continuous black body spectrum. These excitations are also responsible for the dielectric response. 
