This question is answered simply by experiments. Experiments in colliders have not been able so far to measure "divergencies" from the Standard Model. Also the ways of detection differ by the kind of DM particle you consider.
First of all, the neutrinos indeed are a part of DM, they consist what we call Hot Dark Matter. The "hot" stands from the fact that these particles decoupled while being relativistic (neutrinos decoupled at temperature T \approx 0.8~MeV so since their masses are small compared to this value, they were relativistic) .
Now the data we have, if I recall well my value is from Planck's data, the effective number of neutrino species is N_{eff}=3.3 \pm 0.27 (here you can find more on these:
http://resonaances.blogspot.de). Comparing to the result one obtains by taking into account finite temperature and decoupling effects and Standard Model predictions, N_{eff}= 3.046, you can see that in general they are in par. However this also can allow for extra flavors of more massive particles (in case they are fermions, they are called sterile neutrinos). I don't know exactly how can someone look at them in colliders (maybe by looking for new leptonic processes)...
For example the Supersymmetry gave a candidate for DM, mainly named neutralinos (Lightest supersymmetric particles). For their detection in colliders you get the actual signal and a signal coming from the known Standard Model processes. If you subtract the SM from that signal you can look whether you have an excess of events (coming from new physics) and determine its statistics (whether the excess appears as statistical fluctuations). So far there has not been a detection of such an event excess in the colliders. Mainly we are looking at large missing momenta from the detector, and processes that are not favored in the SM. That is why these particles have not been observed, and the only things you can do is put bounds on the parameter space (the space of the parameters that describe this particle, such as its mass). Reasons for this non-observations vary, they can be much heavier and thus more difficult to create.
The axionic DM candidates are not searched in a collider. There are several experiments, using their features, that have been conducted to look for them. Especially for the DM axions (cosmological axions), their cold-DM-nature depends a lot on the model itself (and what is the relation between inflation reheating and PQ symmetry breaking temperatures or order) and also allows for a certain window of axionic masses (approximately from 10^{-6} \text{to} 10^{-3} ~eV). For that you need more information about inflation (eg BICEP2 and we are also expecting for Planck's data). In particular depending on the order of the Peccei-Quinn symmetry breaking and inflation, you can have domain walls and strings forming as topological deflects or you may have just one vacuum homogenized by the inflation. Now back to searches of axions, ADMX (microwave cavity experiments) is such an experiment and it exploited the axions' property of coupling with the electromagnetic field. So far they haven't been able to observe an axionic signal, and so they have been only able to put boundaries on its couplings/mass. Better resolution experiments are being prepared for the future searches. According to Peccei the next 10 years there will be more dedicated works in looking for that invisible particle [of course that's a personal opinion].
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