How do report my rental income so that it avoids taxation in the US? I live in Denmark, where the rental property is, and by tax treaty such income is only taxable in DK.

Are you a U.S. Citizen or green card holder with an SSN or ITIN?

I assume that you are a US citizen living in Denmark?  

If so, I am concerned to see in the Technical Explanation (Article 6 Paragraph 1) where it states:

This Article does not grant an exclusive taxing right to the situs State; the situs State is merely given the primary right to tax. The Article does not impose any limitation in terms of rate or form of tax on the situs State, except that, as provided in paragraph 5, the situs State must allow the taxpayer an election to be taxed on a net basis.

Not knowing the nature of the income, it appears that it should be taxable on the Federal income tax return.  Perhaps you should consult with a professional with expertise in this area.

You may find it to be to your advantage to report the rental income and qualifying for a foreign income exclusion or foreign tax credit.

@uffeH