Certainly you would have to decide on your position regarding the issues that Swift addresses in his essay before composing the letter, but the following ideas may provide a contextual platform as a foundation for the letter.  Swift likens people to "breeders" early in the essay so you could write the letter from the perspective of a company that breeds to explore the aspects of your position.  Similarly, Swift moves on in the satire to suggest that unwanted children are good for eating, so one could take on the role of a restaurant or food-source company to explore this issue.

In the above, I am assuming that through the business letter, you as the writer would need to take on the persona of a business.  However, if you are simply meant to maintain your own persona while using the format of a business letter, you would need to identify points of agreement or contention in Swift's argument as compared to your own to explore in the formal style of the business letter.