Computational methods to obtain relative energies of electronic configurations of atoms
The different occupations you suggest correspond to different spin states. Therefore, they are quite simple to distinguish.
On the other hand, the ground states are often degenerate (in the terms of 5 equivalent d orbitals available). Therefore the lowest (and sufficient) level of theory is the CAS-SCF with inclusion of the s- and d- orbitals.
I tried several calculations using ORCA in def2-svp basis and the results correspond to what one would expect, the time to perform the calculations is in order of seconds.

Zr (should be $4d^2$ $5s^2$, ie. MULT=3)

    CAS-SCF STATES FOR BLOCK  1 MULT= 5 NROOTS= 1
    ROOT   0:  E=     -46.4247189198 Eh
    0.62280 [     0]: 211110
    0.37690 [     2]: 211011

    CAS-SCF STATES FOR BLOCK  2 MULT= 3 NROOTS= 1
    ROOT   0:  E=     -46.4308999710 Eh
    0.49082 [     0]: 221100
    0.47988 [     2]: 221001
    0.01125 [    18]: 210111
    0.00276 [    27]: 201120


Cr (should be $3d^5$ $4s^1$, ie. MULT=7)

    CAS-SCF STATES FOR BLOCK  1 MULT= 7 NROOTS= 1
    ROOT   0:  E=   -1043.1949498785 Eh
    1.00000 [     0]: 111111

    CAS-SCF STATES FOR BLOCK  2 MULT= 5 NROOTS= 1
    ROOT   0:  E=   -1043.1559672632 Eh
    0.40000 [    15]: 111111
    0.30000 [     0]: 211110
    0.30000 [    30]: 011112


Nb (should be $4d^4$ $5s^1$, ie. MULT=6)

    CAS-SCF STATES FOR BLOCK  1 MULT= 6 NROOTS= 1
    ROOT   0:  E=     -56.3066169626 Eh
    0.96220 [     0]: 111110
    0.03771 [     2]: 111011

    CAS-SCF STATES FOR BLOCK  2 MULT= 4 NROOTS= 1
    ROOT   0:  E=     -56.2843641219 Eh
    0.89474 [     0]: 211100
    0.04255 [     2]: 211001


The lower the energy the better. 

From the numbers I'd conclude that it is possible to obtain the ground state configuration by reasonably simple quantum chemical calculations. Nevertheless, I'd expect also less elaborate theories to predict such a fundamental properties.

Edit: I added the multiplicity to the expected ground state configuration