FIP discount and FIP coupons are only valid on NS services, which are practically all intercity services to Maastricht and Heerlen, as well as the Maastricht to Liège train, even though it's operated by an Arriva EMU. It is NOT possible to buy a FIP discounted ticket from Heerlen (or even Aachen) to Liège however, as the part between Aachen and Maastricht is operated by Arriva themselves who do not accept FIP facilities. In this case you would be fine buying a full fare ticket from Heerlen (or Aachen) to Maastricht and combining it with a FIP discounted ticket from Maastricht to Liège or NS and SNCB boxes. The local trains in the region (Maastricht Randwyck - Roermond/Kerkrade, Sittard - Heerlen, Roermond - Venlo - Nijmegen) are Arriva operated, as well as the RE train Aachen - Heerlen - Maastricht (which continues to Liège as an NS operated train to the border and from the border as an SNCB operated train). Rover tickets for buses and trains in the region are available for off-peak travel (Peak hours are Mo-Fr 06:30-09:00 and 16:00-18:30 for trains and 04:00-09:00 for buses, no restrictions on Sa and Su), such as this one for everything operated by Arriva south of Roermond, including cross-border to Aachen:
https://product.arriva.nl/eticket/d?ticket_type_id=77.
It's also available in ticket machines and on buses (though make sure to ask for
train and bus), card payment only. And presumably possible to buy with cash at Arriva ticket offices.
Buying FIP discounted tickets is only possible at NS ticket offices, as mentioned already there is one in both Amsterdam and Maastricht. Even though Arriva ticket machines sell tickets to everywhere in the country, Arriva ticket offices don't, so it's not possible to buy FIP discounted tickets there.