I own a rental property which is rented at well below fair market value. Expenses equal two months rent income. Is it considered a not for profit rental?

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Simple answer: no, since you are actually showing a profit.

That said, for a more accurate answer, we need to know more info.

Why is it rented at well below fair market value? If family is your tenant, you usually don't have a rental, you have a 2nd home.

Does "expenses equal two months rent income" include everything (mortgage interest, taxes, insurance, maintenance & repairs, and most of all depreciation)?

Just because you're renting below FMRV does not mean it's not-for-profit. If you have "ANY" cash flow, then it's probably considered for profit. Take special note that the principle part of your mortgage payment is "NOT" a deductible expense. Only the interest is deductible.