> I would like the columns divided according to rules that would align the columns with my credit cart statement dates, which happen to be from the 10th of a month to the 9th of the following month.
Ahh, I see - and yes, filters wouldn't work for that.
Unfortunately, the standard Pivot Table features won't work either - they're based on calendar dates (years/ quarters/months) and not arbitrary dates.
The easiest solution is an additional column in your source table that maps to the statement the charge falls in to.
For example, I created a simple transactions table containing a transaction Date, Category and Amount.

To this, I inserted a new Column B to be used for the statement date:

The formula in B2 is:
=EDATE($A2,IF(DAY($A2)≤9,0,1))
EDATE() takes a date (in this case, the value in cell $A2) and adds an offset of months to determine a new date. I check the DAY() of the date and if it's ≤9, I add 0 (keep the current month), otherwise add 1 (it's billed on next month's statement.
Filling this down the column and formatting it to show Month and Year only, I now have a column that tracks which statement each transaction is billed to. You can incorporate this statement date into your Pivot Table rather than the raw transaction date:

And here are my Pivot Table settings:

Note that I've added Statement twice - one for 'Year' and once for 'Month', since transactions after December 10th of any year will fall into next year's statement. If I'd just used 'Month' it would calculate late-December charges in the 'January' row, merged with last year's expenses.
You could also use Statement once, with a 'Year-Month' setting and get a single list, but I prefer breaking out the years for visual purposes.