Loop through range with
if Entry < 19600000 then counter = counter +1

provided that Entry is Long, not Int

Try this

Sub CountBirthday()
i = 1
Count = 0
With ActiveSheet
Do While .Cells(i, 1) <> "" 'assuming datas are on column 1 (A)
If Left(.Cells(i, 1), 4) < 1960 Then 'count the number of
person born before 1960
Count = count  + 1
End If
i = i + 1
Loop
.Cells(i, 1) = Count 'display result on last row of column A
End With
End Sub

You don't really need vba for this; assuming the column of figures
below is in cells E23:E27 then
=COUNTIF(E23:E27,"<19600000")
in any other cell should work