Gluon radiation from a nucleon? Due to the fact that neutrons and protons consist of quarks (i.e. are not really Dirac particles), their magnetic moments differ from the so-called nuclear magneton (i.e. the natural unit for expressing magnetic dipole moments of nucleons).
In fact, a neutron has a finite magnetic dipole moment despite being electrically neutral: this is because its internal structure consists of electrically charged quarks.
Therefore, a neutron could be accelerated by electromagnetic fields even if its electric monopole is zero. Moreover, it should radiate photons when accelerated (even though I do not see this fact discussed somewhere... maybe because the effect is extremely small?).
Now the question is: does the same kind of radiation should be expected also for the colour charge?
The "colour monopole" of a nucleon should always be zero, as the electric monopole of a neutron.
However, is it possible to define a "colour dipole" for a nucleon? Will nucleons radiate gluons if accelerated?
Note: I am trying to push the analogy with the neutron that radiates photons despite being neutral: by analogy, we could expect nucleons to radiate gluons despite being "colour neutral".
I suspect that this is impossible because the "ninth" colourless gluon does not exist, see also this question.
EDIT: It seems so, at least according to this paper. However, I do not grasp the technical details. Maybe someone could comment on this reference and explain if it is really relevant.
 A: The radiation for a neutron in a magnetic field has bravely been calculated.
They conclude:

The calculations in this paper are mainly of theoretical interest, as good pedagogical examples in the classical and quantum theories of radiation. Physically the process  is not observable,because the radiation rate of the neutron is very small,

They give an estimate, where the lifetime of transitioning from an excited state is larger than the age of the Universe.
Now for color strong forces, there is no equivalent  macroscopic magnetic field at low energies . The strong color force is within then nucleons and hadrons. The strong nuclear force is a spillover force, corresponding to the spillover van der Waals "wdW" forces in electromagnetism. The quantum mechanical explanation for the "wdW" force  involves virtual photon exchanges, as all electromagnetic interaction examined at the quantum level.  In an analogous way, the spillover force for the strong nuclear will have virtual gluon exchanges between adjoining nucleons, but not something that can be called radiation.
A: Interesting analogy between the magnetic dipole moment of a neutron and the strong force. However, the two are very different. Anna v has already discussed the issue of the radiation of photons from neutron, so I'll just say a bit more about the strong force.
Fundamentally, the force among the quarks is described by quantum chromodynamics (QCD), which is a non-abelian gauge theory. It behaves differently than the abelian gauge theories, such as quantum electrodynamics (QED), which governs the behavior of photons. The important difference is that QCD is confined. What this means is that it only exist inside small regions of space with a size roughly given by the size of a proton. If a gluon would try to leave that space, the force with which it is pulled back to the region increases with the distance. This is opposite to the way it works in QED where the force decreases with distance. So increase the distance for the gluon to radiate away from that region, one needs to put in more energy. Eventually, there would be enough energy to create a new color neutral region that would then separate from the previous region in which the gluon, together with all the other particles created by the separation energy, would be confined. These separated confined regions manifest as jets in high energy collider experiments. (Anna v may be able to say more about this.)
So, as a result, a single gluon cannot be radiated away from a proton or neutron.
A: 
In fact, a neutron has a finite magnetic dipole moment despite it is neutral ... Therefore, a neutron could be accelerated by electromagnetic fields even if its electric monopole is zero.

Dynamics of motion
When light falls on a particle moving in the same direction, this particle is accelerated. If photons are not completely absorbed, they are re-emitted with lower energy (red-shifted). This also applies to neutrons. Kinetic energy can be transferred from photons to neutrons.
Of course the reverse process also takes place. If a moving neutron is stopped, either by an obstacle or by light entering in the opposite direction, the loss of kinetic energy is released in the form of photons.
For this cognition it is enough to think in classical mechanics. No quarks or magnetic moment is necessary.

Moreover, if a neutron is accelerated I expect it should radiate photons

Quantized interaction with photons
Bonded neutron (more precise not free in all axis) interacts with the surrounding particles. When the neutron is hit by a photon it may gain kinetic energy. Some part of this energy it may transfer to the surrounding particles and some part it may re-emit. In this sense the neutron radiates. For a free neutron my feeling is that the neutron is not able to absorb at once any photon. The more energetic the photons are, the more likely it is that a part of their energy will be released as radiation again.
Induced radiation
The statement that charged particles radiate come from the Lorentz force experiments. A moving charge, influenced by an external magnetic field, gets deflected. During the deflection it radiates and loose kinetic energy.
Electric and magnetic fields do not interact. The conclusion is, that the magnetic dipole of the charge and the external magnetic field interact. The external field try to align the charges magnetic field. During this alignment the charge radiates a photon (the particle gets deflected a bit). The emission of the photon disalignes the charges magnetic field again and this process repeats until the kinetic energy is exhausted and the particle comes to rest in the centre of its spiral path.
The interesting question is, will the same happens with a neutron. A question about this was deleted on PSE, it hasn’t answers.
A: Radiation from a nucleus is discussed. For example x-rays are emitted from electrons and Y rays are emitted from the nucleus. https://www.sciencedirect.com/topics/physics-and-astronomy/gamma-radiation
There are even interesting articles about the field that is formed by photons emitted from the nucleus and how it affects the arrangement or separation of the electron shells.
