With marine fish you get very bright, solid-looking species so I would aim for similar fish.
I have thought about this before and came up with female bettas (or a single male), male dwarf gouramies (not with bettas), rainbowfish but for smaller tanks you would probably be looking at neon/blue dwarf rainbowfish in particular(threadfins too but they aren't as bright), peacock gudgeons, purple spotted gudgeons (for slightly bigger tanks), an opaline gourami (again, for the slightly bigger tank and not with bettas), platies, swordtails, clown rasboras, fire rasboras, khulie loaches, gold zebra loaches (for the bold markings but small size), tiger barbs (school of at least 7 in at least a 20 gallon though), a red tail black shark (bigger tanks) or rainbow shark and possibly some guppies/mollies or endler's though the guppies and endler's, IMO, look too fragile to be marine.
Obviously, if you have the tank for it, discus look marine and larger rainbowfish are great too. There's all sorts of gudgeons/gobies that are brackish or freshwater that are closely related to marine fish and several species of african cichlids - especialy mbuna - have colors similar to marines but require a bigger tank to be at their best. I don't know what your opinion is on this but I feel rams and apistos and other dwarf cichlids, though they have the color, don't have the 'substance' or that 'solid' look marine fish tend to have.
In a 15-20 (US) gallon, I'd probably get 4 female bettas with a couple of khulie loaches and a small school of blue dwarf rainbows.
Otherwise, a set-up based around peacock gudegons would be wonderful with some schooling fish to balance it all out. Maybe a dwarf gourami as well.
Something else to consider is that marine reef set-ups tend to have few fish with lots of invertabrates. Brightly colored or unsusual shrimp (like cherries) might, therefore, be nice additions to a freshwater marine-look-a-like tank. As would an apple snail etc.
You'd also want a sand substrate and rock to make the tank look reef-like and you would probably want to avoid adding plants as they would probably make you think 'freshwater'.
