Which tree won't drop sap or berries?

Hi everyone.  We've just moved to a new estate and have quite a shallow wide garden.

I'm looking for a tree that I can put next to the fence opposite the living room to add a little privacy as we are overlooked.  Ideally something that LOOKS similar to a cherry tree (i.e your "traditional" tree) but that won't drop sap or berries as on the other side of said fence is the neighbours' garages and I don't want their cars damaged by sap or berries etc.

Many thanks in advance.

Amelanchier are lovely trees - they do flower and fruit but in our garden the birds have a feast !

Pam x

Many trees that produce berries don't cause any problems. You need to avoid the likes of elderberry, but sorbuses, hollies, cotoneasters (the tree forms such as 'Cornubia' ) and the amalanchier mentioned by Lilylouise  don't drip sap and don't drop soft berries that stain.

Elderberries are the worst for berries because the birds eat them and then drop purple poo away from the tree. 

Lime trees, maples, walnuts are some of the worst for dripping sap. 

Hi Lilylouise and Gold1locks - thank you both for your suggestions, they're very helpful (off to google them all!).