I do not know if you have found an answer to this, but a crude way of doing
this would be to iteratively generate random data using beta distributions
where a and b vary. Then test each generated distribution against your
random data using a Kolmogorov-Smirnov test.
The Kolmogorov-Smirnov test is called using ks.test([your data], [generated
data OR a cumulative distribution function])
This should at least give you a range of values for a and b within which
your data falls.
Hope this helps,