How to create custom column in calendar table for 9 day rotating shifts

Basically you wll add a comma to your final step, then add this code (I picked up with your final else clause. Delete everything below that and add this:

    ...
    else [Year]),
    varRowCount = Table.RowCount(#"Added Custom2"),
    varListNeeded = 
        List.FirstN(
            List.Repeat(tblCycle, Number.RoundAwayFromZero(varRowCount / 9)),
            varRowCount
        ),
    CombinedWithCycleList = Table.ToColumns(#"Added Custom2") & {varListNeeded},
    BackToTable = 
        Table.FromColumns(
            CombinedWithCycleList, 
            Table.ColumnNames(#"Added Custom2") & {"Cycle"}
        )
in
    BackToTable

This assumes the Cycle data (1st, 2nd, etc) is in a list called "tblCycle" - see how I did it in Excel.

If you have a file you can share, I can help you connect it. Or you might look at the blog post at the end of these directions.

How to use M code provided in a blank query:
1) In Power Query, select New Source, then Blank Query
2) On the Home ribbon, select "Advanced Editor" button
3) Remove everything you see, then paste the M code I've given you in that box.
4) Press Done
5) See this article if you need help using this M code in your model.