I've been writing my second story in a series while trying to promote the first. Would you consider it to be acceptable to request buyers of the first book to post an online review, and offer them the opportunity to name a character in the next title in the series?
I think that's perfectly acceptable, so long as it's optional. That sounds like a really interesting way to gather reviews. The only thing I might make sure to do is assure them that they should write the review really based on what they think and felt about the first book.
If you have an active facebook page a better way to market might be to get people to like and share your first book to give them an opportunity of appearing as a character in the second. That's what i'll be doing with mine.