Maybe you'll find the staircase you look for in Trimble 3D Warehouse?
Note that Sweet Home 3D furniture import wizard supports DAE/Collada format but not SKP/SketchUp format. So if the model you prefer is available only in SKP/SketchUp format, you'll have to convert it to DAE/Collada format by choosing File > Export > 3D Model... out of the menu in the free version of SketchUp.
If you want the imported staircase to automatically create a hole in the floor of the upper floor, you'll have to check the Staircase option at the third step of the furniture import wizard. If the default hole doesn't match what you want, the easiest way is to draw a room at the upper floor that will show the hole you want.