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No corals in a one gallon? Where have you been the last 5 years man
After your initial setup is cycled and you are absolutely sure of temperature and specific gravity trends you can keep any coral that will fit in it. I would stay away from heavy feeders like cup corals. Corals that work for sure in one gallon systems that are stable (insofar as one gallons get) are: mushrooms, candy coral, small hammer coral and frogspawn heads, some SPS montipora I've been able to grow for years (many others do too), all sorts of zoanthids and button polyps, and xenia to name a few. They do not overtake the system at a frankensteinish rate, I love xenia in my pico reefs due to the movement. Do water changes often to replenish your lost elements, clip them when they grow too big, if you plan on keeping dense coral loads I recommend you dose small portions of any two-part system at least 2-3x per week. Dose nothing else but that and some high quality frozen food just before your 90% water changes at least bi-weekly... This reef below is 1/2 gallon, it demonstrates the range of life that can be kept in stable systems. Keep your salinity and temps to a T
this closeup shows brown SPS growth (but still asexual reproduction/growth nonetheless) and the density of corals that can be kept in pico systems.
The shot with the hand in it shows the total size...about 8 inches long and 4 inches tall. You can also see Porites, Hydnophora, some soft corals and many other stony ones. The common assumptions of allelopathy between coral systems don't apply much in the aged pico reef, I think in time there are sensitization pathways that reduce the output of dangerous chemicals and nematocyst nettling characters. How else can this be growing?