Both mollies and puffer fish require an intermediate level of aquarium skill. Their demeanor and ideal aquarium requirements make them a bit more of a challenge than typical "beginner" fish. However, some species of puffer have similar care requirements to mollies and may make good tank mates, with some caveats.
When pairing puffers with mollies, temperament could pose a problem. Mollies are very easy-going aquarium fish. Most, but not all puffers display some degree of aggression towards tank mates. Always research the specific species of puffer fish you want to keep. Additionally, even the more docile puffers are inveterate fin-nippers. Such fish generally target fish with long, flowing fins. Some species and varieties of mollies have such fins. Any mollies that share a tank with a puffer should belong to a short-finned variety, since it makes them less of a target.
Mollies actually come from brackish water -- water with some salt in it, but less salt than full-strength seawater. Some common puffers also come from brackish water, which makes them well-suited for sharing an aquarium in this respect. However, different species of puffer fish have different preferred water conditions. Always research the exact species of puffer you are looking at to ensure that it can tolerate brackish conditions. Freshwater puffers find salt stressing. Meanwhile, mollies tend to not thrive unless there's at least some salt in their water. For example, the dwarf Indian puffer fish would make a decent tankmate for a molly, but it comes from pure freshwater and tolerates salt poorly.
You can set up your tank to make things go more smoothly in a tank with both mollies and puffer fish. For example, if you densely plant the aquarium with silk or plastic plants -- most live plants cannot survive in brackish water -- you can give mollies hiding places from their puffer fish tank mates. Visual barriers help decrease aggression. However, make sure the tank layout also includes some areas where mollies can school in open water.
Best Case Scenario
To best ensure your mollies will get along with your puffer fish, you should carefully select each. Several species of mollies are available, and most come in a least a few varieties. Avoid species with long, flowing fins like sailfin mollies. With this in mind, several common puffers make good tank mates for mollies. Both the green-spotted puffer (Tetraodon nigroviridis) and the figure-eight puffer (T. biocellatus) prefer similar water conditions to the molly and will rarely pick on active fish with short fins.