The simple answer is yes, you may invest in individual stocks and bonds.  But you may not want to do so.

The standards for investment decisions are generally set by the Prudent Investor Act and the newer Uniform Prudent Management of Institutional Funds Act.  (See Ready Reference Page:  “New UPMIFA Sets Rules for Management of Charitable Funds”)  Basically, a director or trustee of nonprofit investments is required to act “in good faith and with the care an ordinarily prudent person in a like position would exercise under similar circumstances.”  They can consider a whole lot of different factors in making their decision, but are required to diversify unless otherwise provided in a gift instrument or because of “special circumstances” that better serve the purpose of the fund.

The November 20, 2014 issue of the Chronicle of Philanthropy has a special section on endowment investing, highlighting a wide range of different investment policies.  It is clear under the law that investment managers may consider the recommendations of their professional advisers, but are not required to do so.  (See: “Trustee for Charity Must Invest Income-Only Fund for Growth")

There is no single program for investing.  You may want to make a portion of your investments in specific situations for programmatic purposes, like a community foundation investing in local stocks to boost the local economy.   But if your board members are not professional managers, you can buy that professional management, and a great deal of diversification, by buying funds, including funds with socially responsible investments.  The key is regular monitoring of the investments against relevant benchmarks and against your investment objectives.