first, to declare a variable in vbscript you have to use the "Dim" keyword.
Second, in vbscript you must declare a variable first before using it.
So either on two lines or on one line with a colon as end-of-line separator.
Dim Counter : Counter = rs("Counter1")
Since you use it in a loop, declaring it separately is the obvious choice.
The following should work for you:
Set rs = connDB.Execute("sp_GetCounter")
If not rs.eof Then
Do until rs.eof
Counter = rs("Counter1")
Set rs = Nothing