Your problem is that mudskippers live where there are very few fish. They are poor swimmers, so if they lived where predatory fish were common, they'd be eaten. Instead, mudskippers live where the water is very shallow and others fishes cannot go. So, if you put mudskippers in a tank with active fishes of similar or larger size, the mudskippers get scared and will avoid the water. This holds true even where the bigger fish are harmless, like monos and scats.
Archerfish
can work well if the mudskippers are of equal size, but it is rare for this to be the case. Normally, archers are sold around the 8-10 cm mark, while baby mudskippers aroud the 4-5 cm mark seem to be the most commonly traded. But if you can get a large mudskipper species, like P. barbarus, and a smallish archer, like T. microlepis, then the combination would be worth trying. An SG of 1.005-1.008 would suit both species. T. microlepis don't like SG above 1.010, and ideally not even that. The smaller mudskippers only get to about 10-15 cm, are are going to be terrified of the larger archer species like T. jaculatrix.
The other fish worth trying would be the sailfin molly. These like saline conditions, and mollies tend to be pretty harmless fish provided they are not overcrowded.
One last thing. Mudskippers are completely indifferent to water quality (though water chemistry is important). Archerfish and mollies, on the other hand, should be given good, clean water as well as plenty of swimming space. If I were mixing mollies with mudskippers, I'd be thinking about a 180 litre aquarium, half filled with water, with lots of rocks and bogwood for the mudskippers. Giving the "swimming" fish like the archers and mollies too little swimming space would be bad in the long run, partly because they'd feel confined, but also because of the inability to keep the water clean if they only had a few tens of litres to swim in.
Cheers,
Neale
I really want another fish in with them if I do do mudskippers. What about Archerfish? Also, how would I take care of them and mudskippers?