I know there are other ways, but this should work you'll have to play around with the cell reference.
Use a named cell reference in to indicate the end of your sheet. Use that reference in the Macro, then offset and insert the copied cells. do it so the named reference gets pushed to the bottom every time.
This sort of works (below) I didn't have time to get it to work properly.
It opens a file copies a range closes the book then opens the destination book selects the named reference and pastes (thats the part you'll have to play around with)
Workbooks.Open Filename:="C:My DocumentsKNROW COUNT.XLS"
Range("A1651:A1665").Select
Selection.Copy
ActiveWindow.Close
Workbooks.Open Filename:="C:My DocumentsKNcopypastetobottom.xls"
Range("blankline").Select
''ActiveCell.Offset(-1, 0).Range _("blankline").Select
Selection.EntireRow.Insert
ActiveSheet.Paste
Selection.Insert Shift:=xlDown
Hope it helps
Ziggy