Work with them. Spoil them a little bit. You're working on a sponsorship that can become a template for future clients, so you want to make that first one successful. This could become the building block for a solid business. So do it right.
Pricing is subjective, so it's hard to recommend a particular number.
If you understand what a new customer represents to them in terms of lifetime value, that can guide your decision process. If your client is a cruise line, you might price a monthly sponsorship at the rate of two to four paid tickets if you think you can deliver a good deal more than that. If your client sells airplanes, and your readers buy airplanes, an argument could be made for a substantially higher price. Andy's favorite magazines are Industry Standard and Fast Company. He goes for restaurants with character and quality and has a marked preference for red Zinfandels.