Ordinarily, it is legal for a charity, including a church, to sell real estate and invest the proceeds in a quasi-endowment to generate income for its mission activities.  Most frequently those investments are a diversified mix of publicly traded securities. The gain from the sale of the property, if any, is not subject to federal income tax and the income from the investments, including profits from reasonable trading, is not subject to unrelated business income tax (“UBIT”).

You have thrown a wrinkle into the mix by talking about investing in real estate, however.  Income from the rental of property that is not related to the reason for which you are tax-exempt is subject to unrelated business income tax if the property is subject to “acquisition indebtedness” or if you provide personal services beyond normal landlord-tenant services like cleaning the public areas of an apartment house.  (See Ready Reference Page: “Nonprofits Often Worry About UBIT”)

You can obviously purchase more real estate if you use the leverage of a mortgage, but you are likely to lose some of the income to UBIT (in addition to what you have already lost to local real estate taxes).  As a church, you are automatically considered a public charity and not a private foundation.  But an organization that obtains public charity status by virtue of its broad-based public support could lose its publicly supported status and be reclassified as a private foundation if it has “too much” unrelated business income.  (See Ready Reference Page: “Calculating Public Support”)

You haven’t indicated what other income or assets you may have to support your missions or what portion of your total budget this investment would generate.  You haven’t indicated whether you are experienced in property management. 

The specific answer to your question is: it is legal for a charity to reinvest the proceeds of the sale of a building in real estate.  But real estate is not a buy-it-and-forget investment.  It does not necessarily yield a constant stream of cash flow for you to spend. You should estimate carefully the return you can reasonably expect, especially if you intend to purchase the property with one or more mortgages, and compare the estimated net return to the risks and headaches that will be involved.  Then you can consider whether it makes sense to do.