May the board of a 501(c)(3) charity designate some of its funds to be used for "board appreciation" or even "board and staff appreciation?"
The answer to your specific question is “yes.” The board already designates funds for salary for the staff, and it regularly does little things to thank the board and other volunteers. So long as these are of reasonable value, they are clearly within the acceptable costs of meeting the organization’s mission.
Your unasked second question, however, is how the recipients (and the organization) should treat the “appreciation” for tax purposes? The general rule is that payment of cash for services rendered (which is the basis for the appreciation), including for the volunteers on the board who don’t expect compensation, is considered compensation and is taxable income. The IRS has made exceptions for gifts of property of nominal or incidental value, things like holiday turkeys or hams, or recognition plaques or pins. The IRS says that those gifts can be disregarded and treated as non-taxable gifts. If the recognition is a gift card or similar item readily converted into cash, however, the distribution is taxable income.
To make things a little more worrisome, you should realize that a taxable payment made to a disqualified person, which includes everyone on the board, can be treated as an automatic excess benefit for the recipient if is not treated as compensation at the outset. It could also be a taxable act for an organization manager who knowingly approves it.
So, yes. You can spend for board and staff appreciation. Just be sure you handle the appreciation and its taxability appropriately.