Predicting orbital angular momentum effects on magnetic moments
When do exceptions to this behaviour occur ? For example I have found that $\ce{Co(bipy)_{3}(ClO4)}$ has a lower experimental magnetic moment than the spin only formula predicts despite being a $\ce{Co(I)}$ (d8) compound with a $^{3}\!A_{2g}$ ground state, but I do not understand why.


According to ADVANCES IN INORGANIC CHEMISTRY AND RADIOCHEMISTRY, Volume 12, page 193 "The tris(bipyridal) cobalt(I) cation has a magnetic momment of 3.2-3.4 B.M. which is independent of temperature from 70K to 340K".

Since there are two unpaired electrons, the spin only value is $\sqrt{2(2+2)} =2.83$.  So your experimental data are inconsistent with the literature, as 3.2-3.4 is greater than the spin only value, 2.83.


  Is the deviation from the spin only formula always positive for $T$ states ? If not can we predict its sign similarly ?


No, the deviation from the spin only value is not always positive for complexes with T ground states. The main characteristic of complexes with T ground states is that the magnetic moment is temperature dependent, because the spin-orbital coupling splits the T state into states that differ in energy by an amount close to kT.  

For example $\ce{Cs2VCl6}$ has a magnetic moment of 1.4 at 80K and 1.8 at 300K, with the spin only formula predicting 1.73.  So deviation can be negative, and isn't necessarily positive or negative even for the same compound, depending upon temperature.  

See section 4.3 of Dr. Mark D. Spicer's magnetism lecture for more information.