Why is MP2 failing to calculate proper IR frequencies for [Co(CO)4]- and [Fe(CO)4]2-?
Some months later but here we go...

I agree with most of the comments that multiconfigurational effects should be present for this system, and maybe they are very strong. But I tend to think that this is not the cause of the huge difference with experimental values. The fact that B3LYP returns reasonable values should be taking into account. Surely it "could be" just a coincidence but let's face it, I is very unprovable that all the results are reasonable due to coincidence (it is very simple to check it out, just try some others well proved functionals).

My guess is that you found the correct nuclear coordinates for the minimum of the PES, but the SCF part of the calculation have serious problems and it converged to some unreasonable electronic "state". This would imply that the MP2 results are ridiculous.
As HF and B3LYP are very different in the SCF part, B3LYP converged correctly.

You could try different initial guesses (Hückel, PA, a previous converged calculation) and different methods (like RHF, OHF, UHF etc.). Other basis sets can also help (a little larger if possible). I would try to avoid effective core potentials! (I understand that this can be a problem for your teaching purposes). Convergence method is of course of main importance (consider quadratic or very damped convergence) . I found almost impossible that calculating inner electrons correlation helps in this case.

Of course that the refinements that you tried are useful, but I think that just to improve quantitatively the results.

I hope that the ideas above help you. I would like to know if you effectively solved your problem.

Regards