I can add rows conveniently using Option+Shift+Up Arrow (insert above) or Option+Shift+Down Arrow(insert below).
Is there a keyboard shortcut to delete the current row?
You can create one yourself though:
Open System Preferences → Keyboard → Shortcuts → App Shortcuts.
Click the + button to add a new shortcut.
Set the Application to Numbers.app, and the Menu Title to Delete Row.
Set your keyboard shortcut and press Add.
As of at least Numbers 4.3.1, there is a menu item in the Table menu for deleting the current row (as well as one for deleting the current column), with keyboard shortcuts:
Delete Row: Shift+Command+X
Delete Column: Shift+Command+Y
As others said, but with correction:
First, follow process from ABOVE
SECOND: Quit System Settings and Numbers app and RELAUNCH. Without relaunch, shortcuts do not work for some reason.
This is for latest Numbers as of May 2019 (version 5.3 - 5989)