I think it will help you.
http://www.honeywell.com/sites/docs/doc3b3098-fc16b62244-7b26ceabff4f164327109b1662bcc80d.pdf
Neutron diffraction. The scattering cross section for oxygen is much higher than with x-rays. This is a very common way to determine oxygen stoichiometry and site occupancy (as well as any oxygen ordering) in perovskites. I've used this method to determine the oxygen site occupancies in copper oxide based pervoskite high temperature superconductors and was even able to see long range oxygen ordering which led to a super-cell which is approximately 20-30 times larger than the basic unit cell, if my memory is correct.
No instrumental method will give you better accuracy in determination of the oxygen nonstoichiometry than good old chemical analysis. Specifically, you will need to perform the ox-red titration. Typical procedure includes dissolution of the sample in the excess of the reducing agent (for example, acidic solution of the Mohr's salt is suitable if B=Mn or Co) and then obtained solution is titrated by KMnO4.
Search using keywords like 'oxygen nonstoichiometry titration' will give you lots of articles with different variations of this analysis, so you can choose what is the most convenient in your case.
Alexander is right, the best way to find out a value is to measure it directly. Also a microprobe analysis can provide an answer (normalizing the structural formula to 2 cations), but is affected by uncertainties induced by polyvalent cations - hopefully you don't have them, as usually is the case in natural perovskite. From what I know, also natural perovskite does not have the bad habit of being oxygen-defective. Yet, there are a lot of perovskite-related synthetic structures which are "defect perovskites".
Another way to determine the Oxigen could be the Wavelength-Dispersive X-Ray Spectroscopy (WDS) that allows to discriminate the element stoichiometry of materials.
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