Figured out my own question so I'm posting the solution.
Turns out I was on the right path all along and had actually got it working (with errors) However while researching the issue I found by simply adding Application.EnableEvents = False to the beginning and true to the end solved my problem and everything works now.



Dim CellX As Range
Dim listofcells As Range

Set listofcells = Range("E7", Range("F7").End(xlToRight))

Application.EnableEvents = False

listofcells.Offset(1, 0).Clear

For Each CellX In listofcells
CellX.Offset(1, 0).Font.Bold = True
CellX.Offset(1, 0).HorizontalAlignment = xlCenter
CellX.Offset(1, 0).Borders(xlEdgeLeft).LineStyle = xlContinuous
CellX.Offset(1, 0).Borders(xlEdgeRight).LineStyle = xlContinuous

If CellX.Value = 1 Then
CellX.Offset(1, 0).Value = "DUTY"
CellX.Offset(1, 0).Interior.ColorIndex = 6


ElseIf CellX.Offset(-2, 0) = "MON" And CellX.Offset(0, -3) = 1 Then
CellX.Offset(1, 0).Value = "DOG"
CellX.Offset(1, 0).Interior.ColorIndex = 4


End If
Next CellX
Application.EnableEvents = True