David, could you provide your motivations for this question? Personally, I find it easier to rummage up examples where the Eilenberg-Moore category of algebras (over a cartesian closed category) is cartesian closed, than I do for where the Kleisli category is cartesian closed. If you could provide examples of what you have in mind, that could be helpful.
– Todd Trimble♦Aug 27 '10 at 19:18