Is it permissible to design a website or program for a company some of whose work is permissible and some is impermissible, knowing that I will not directly engage in the impermissible acts myself?

If the forbidden outweighs the permissible in the company's work, then it is not permissible to work there. If the permissible outweighs it, then it is permissible. If the forbidden and the permissible are equal, then it is not permissible, giving precedence to the side of prohibition.