This is a very small country Bendigo and the industry has been hard hit over the last 10 years or so, because of the very poor rate of exchange between the Kina and the US dollar. For those who've been here and haven't heard, APNG (previously known as MBA) has closed its' operation at Tabubil. For those that don't understand the significance of this, the industry here is in decline... massively.
NCA is about the only one that a low-timer is ever likely to get a shot at here. Other GA companies are either smaller (with few opportunities for employment) or much bigger (with their own cadetships etc.).
Island Airways at Madang might be a possibility.
PO Box 747 Madang
Fax +675 852 2353
Vanair at Vanimo is about the only other one that you could try.
PO Box 167 Vanimo
Fax +675 857 1272
I'm not confident that either of these will have vacancies and am not up on their requirements. Thus, no guarantees, but a fax doesn't cost much to send. More of a gamble, financially, to come here as a visitor (ie tourist) and go see these companies, but you might get a better reception that way.