If you enter a legitimate date serial number, then "mm/yy" should be a perfectly valid custom number/date format.

https://support.office.com/en-us/art...7-9c9354dd99f5
https://support.office.com/en-us/art...rs=en-US&ad=US

You are correct -- as text, you cannot use number formatting to change the display of the entered text. You can always use Excel's text manipulation functions to change the text string. If you enter '0119 in a cell, an adjacent cell could have a formula like =LEFT(cell,2)&"/"&RIGHT(cell,2) to insert a / in the middle of the text string.

A lot depends on exactly how you intend to use this -- what do you want to enter for data entry, what do you need the output to be, what are you going to use the output for, and so on.