I'd go with the insertion sort solution, but if you want to stick with what you have, the following changes will make it much, much faster:
Code:
    For outer = 1 To ln
        For inner = ln To outer Step -1
            If c$(outer) > c$(inner) Then
                tmp$ = c$(outer)
                c$(outer) = c$(inner)
                c$(inner) = tmp$
            End If
        Next inner
    Next outer