That's a bit of an impossible request - anything which gets tall enough and sturdy enough to be used as a bird feeding station will also have a good root spread. Corylus contorta, for instance, which only reaches 10 feet, has sturdy enough branches, but its relatively slow growing, and most birds prefer a higher spot to feed from. Amelanchier 'Ballerina' might fit the bill if you buy a taller one to start with.

Maybe I should have said roots that stay underground so neighbours do not complain,there must be something.

What is the tree you are having to remove - is it a cherry by any chance? And is it because the roots are near the surface?
How close is the tree currently to your house and the neighbour's house, roughly?

It's a sycamore and the roots are starting to come up in the neighbours garden but not mine. It's well away from both houses.

Oh well, sycamore, much better out than in, in my opinion, far too large for gardens. Smaller trees to consider: Laburnum watereri vossi, Malus Gorgeous, Amelanchier Ballerina, Sorbus Sheerwater Seedling, Crataegus Paul's Scarlet or Crataegus 'Carrierei'. Google for pics and info. Sorbus, Malus and Crataegus attractive to birds anyway, they produce berries or crabapples, all flower.

Thanks for that really appreciate it.