You could also thicken with cornstarch, as you would a pie filling.

I can't find the Hungarian sour cherries I fell in love with years ago, I think I'll be using Wos-Wit sour cherry preserves. They're a local business and I'll have no trouble finding them.
Thanks to everybody for the great suggestions.

I agree with mrslarkin and hardlikearmour- stabilize with jam and gelatin. I would not blend the cherries with any dairy product- except to top with whipped cream. What kind of tart cherries are you using? Fresh, frozen or preserved? If you get the tart cherries in syrup, you can reduce the syrup down and add gelatin as a stabilizer. Fresh/frozen will go beautifully with raspberry jam and some kirsch.

One of my favorite Jacques Pepin recipes is a Chocolate-Cherry Cake from his cookbook The Art of Cooking Vol. 2 (page 226). The filling is made with whipped cream, gelatin, cherries, kirsch, and cherry preserves. You'll have to do a little smoothing out once you build the cake, but the gelatin makes the filling pretty stable.

Martha Stewart has a recipe for cherry-jam gelatin, using sour cherry jam. It is for a wedding cake so makes 7 cups. You'd only need to make about a cup for a single layer in a 9-10" cake. http://www.marthastewartweddings.com/recipe/cherry-jam-gelatin

To keep it easy, I'd just beat cream cheese and the sour cherry preserves together for the filling. The cream cheese adds richness, will keep it firm enough to still call filling, and will pair nicely with the preserves without making it too sweet. If you need it sweeter, add a bit of powdered sugar; that will also firm it up even more. Make sure to use the cream cheese that comes in a block, not the spreadable kind. Also, don't try to beat it until it's room temperature (your arms will thank you).