According to the USMC the Harries can operate the AGM-88 and AGM-84, they also can use a older missile the AGM-119 "Penguin".
They would be of easy implementation since they are already in game with the exception of the AGM-119.
The link below refers to the official USMC AV-8B HarrierII manual:
https://www.marines.mil/News/Publications/MCPEL/Electronic-Library-Display/Article/1838570/navmc-350051c-wch1/
Edit#1:
AGM-88
New source:
Page 81
Nordeen, Lon O. (2006). Harrier II, Validating V/STOL. Annapolis, Maryland: Naval Institute Press. ISBN 1-59114-536-8.
Page 30
Wilson, Stewart (2000). BAe / McDonnell Douglas Harrier. Shrewsbury, UK: Airlife Publishing. ISBN 1-84037-218-4.
Could not find the AGM-119 "Penguin" reference but I remember I had it in a book. Harrier does have ASM capability
Harrier have the capability of firing a weapon does not mean it has been used.
OBS.: we have the Mark-77 bombs
Sea eagle being tested