You can add a sizer into the scrolled panel to contain all the buttons. These code should work:
import wx
import wx.lib.scrolledpanel
class GUI(wx.Frame):
def __init__(self,parent,id,title):
#First retrieve the screen size of the device
screenSize = wx.DisplaySize()
screenWidth = screenSize[0]
screenHeight = screenSize[1]
#Create a frame
wx.Frame.__init__(self,parent,id,title,size=screenSize, style=wx.DEFAULT_FRAME_STYLE ^ wx.RESIZE_BORDER)
panel1 = wx.Panel(self,size=(screenWidth,28), pos=(0,0), style=wx.SIMPLE_BORDER)
panel1.SetBackgroundColour('#FDDF99')
panel2 = wx.lib.scrolledpanel.ScrolledPanel(self,-1, size=(screenWidth,400), pos=(0,28), style=wx.SIMPLE_BORDER)
panel2.SetupScrolling()
panel2.SetBackgroundColour('#FFFFFF')
button1 = wx.Button(panel2,label="Button 1",pos=(0,50),size=(50,50))
button2 = wx.Button(panel2,label="Button 2",pos=(0,100), size=(50,50))
button3 = wx.Button(panel2,label="Button 3",pos=(0,150),size=(50,50))
button4 = wx.Button(panel2,label="Button 4",pos=(0,200), size=(50,50))
button5 = wx.Button(panel2,label="Button 5",pos=(0,250),size=(50,50))
button6 = wx.Button(panel2,label="Button 6",pos=(0,300), size=(50,50))
button7 = wx.Button(panel2,label="Button 7",pos=(0,350), size=(50,50))
button8 = wx.Button(panel2,label="Button 8",pos=(0,400), size=(50,50))
bSizer = wx.BoxSizer( wx.VERTICAL )
bSizer.Add( button1, 0, wx.ALL, 5 )
bSizer.Add( button2, 0, wx.ALL, 5 )
bSizer.Add( button3, 0, wx.ALL, 5 )
bSizer.Add( button4, 0, wx.ALL, 5 )
bSizer.Add( button5, 0, wx.ALL, 5 )
bSizer.Add( button6, 0, wx.ALL, 5 )
bSizer.Add( button7, 0, wx.ALL, 5 )
bSizer.Add( button8, 0, wx.ALL, 5 )
panel2.SetSizer( bSizer )
if __name__=='__main__':
app = wx.App()
frame = GUI(parent=None, id=-1, title="Test")
frame.Show()
app.MainLoop()