Honestly, right now with the APer's, it's more of which ones are working. I'm pretty sure the slots are down on neo, so the APer's for them won't work. Dice-a-roo is down too, so the APer for that won't work either. I wouldn't reccomend going for a chance game where you can lose your NP that you earned in the game, like double or nothing. With only 4k, kiss the morthog wouldn't be a good choice because it costs 50 NP, and though you can earn 100 NP on level one, the chance drops from 50% to 16.67% of selecting the right morthog on level 2 (according to Jellyneo's guide). So you'd only earn 50 NP profit on level one, and the other levels don't have a good chance of winning, so you'd be losing all the NP you won from the previous levels if you select the wrong morthog.
Coconut Shy wouldn't be a good option either, as it costs 100NP per try, and you only have 4k. Bagatelle is also based on chance, so I wouldn't pick that either.
I'd recommend the pyramids AP, where you can earn up to 5k a day, and though it costs 50NP per play, you can easily win that back in the game. Cheat may be another possible one, but it can take a long time to beat the level, though you do get NP for catching cheaters. Kacheek seek would be another easy way to get NP, but you get very little from it most of the time, and your pet can get bored playing it.
Basically I'd recommend games that aren't based on chance.
It may take a while, but the NP from the APer's will build up.