typically, you don't have to pay experts a dime... if they are really interested in their field, and in getting their views out there, many of them are actually appreciative of the opportunity to do so on film.
of course, you don't want to waste their time either. your only "payment" to them needs to be an organized production, perhaps a meal or two depending on the length of the shoot, asking good questions, and of course, finishing your film. at the end, they should also receive a complimentary DVD and perhaps an invitation to a local film festival where your work is playing.
don't offer any cash if you can at all help it. if they ask for it, just plead poverty and inform them about the "low-budget" nature of documentary. if they insist on payment, you can just find another expert, or find some other non-monetary compensation that will satisfy them.