How do I report rental income on a 1 week time share we own every odd year?

So you are renting your time share for less than 15 days every odd year.

 

The IRS says in this document:

 

Minimal Rental Use

There's a special rule if you use a dwelling unit as a residence and rent it for fewer than 15 days. In this case, don't report any of the rental income and don't deduct any expenses as rental expenses.

 

So, there is nothing to report about this rental on your tax return.