What should we pay nonprofit director?

Assuming that this request came as a surprise, as I infer from your question (but may only reflect my own sense of shock), my first recommendation is to avoid a charge of assault and battery.  Stand back and take a deep breath before striking out.

It is not illegal to pay directors of nonprofit corporations, but it is very unusual.  You don’t say what type of nonprofit you have, but about 90% of charities do not pay their directors anything.  Payment for private foundations is more prevalent than for public charities, but even there many directors are not paid.

Do your bylaws say anything about compensation of directors?  Many nonprofits provide in their bylaws that directors will not be paid for their services as such but can be reimbursed for out-of-pocket expenses.  Do you promote on your website that the board members are volunteers or have anything about compensation in your statement of expectations of directors?  Is anyone else being paid?  Has anyone else asked for payment, with what result?  Does your Form 990 reflect payments to directors or list all zeros in the compensation box?  In short, did the person claiming compensation have any reasonable expectation of payment?

Assuming you don’t want to pay but don’t have a clear policy statement against it and believe it is a good faith request by someone who reasonably thought they had a right to payment, you could legally settle if you are a 501(c)(3) charity or (c)(4) social welfare organization so long as the payment is “reasonable” and for hours actually worked.  You would need to scrutinize the bill and determine whether the hours were legitimately spent and whether the rate is reasonable for the person and the work done.  (In many large nonprofits where $50,000 might be reasonable compensation, directors are expected to contribute significantly to the organization for the privilege of serving as a volunteer, resulting a negative cash flow situation.)  If no other director is being paid for the same type of work, it could be argued that this requested payment should be deemed unreasonable simply because everyone else is a volunteer.

The claiming director should be made aware that the payments would vitiate the personal protection from liability under the federal Volunteer Protection Act (See Ready Reference Page: “Federal Law Protects Nonprofit Volunteers”) and probably any similar state law.

You should be aware that you could be liable for breach of fiduciary duty to the organization if a member (if you have voting members) or another director of the corporation objects to the payment and the claiming director would be unlikely to win the claim in court.

Even if you have insurance that would protect you against a claim in court, you really want to avoid litigation, however.  Ideally, a settlement will satisfy the claiming director (even if only to understand your culture), set the policy clearly going forward, and not so offend the volunteer directors that they hold a perpetual grudge against the claimant, particularly if the claimant is going to remain on the board. But get it resolved quickly so that it does not become a long-term distraction from your mission, whatever it is.