Neon tetras are known for getting along with most fish. However, they do their best in water with a pH of 6.5 to 7 and require tankmates who will not harass or eat them. Fortunately, there are several bottom feeders that get along great with neon tetras.
Corydoras catfish, also called cory cats, come from the same general region as neon tetras (the Amazon river and its tributaries). Cory cats act more like tetras than most typical catfish: they school and are active in the daytime. But they still scavenge from the substrate and help eat extra food like a helpful catfish. A large number of species are available, including the peppered cory, the bronze cory and the julie cory. All have similar care, though you have many different patterns to choose from.
Plecos are what most people think of when they think of bottom feeders. There are a number of very different fish in this family, ranging from a few inches to a few feet in length. You must be careful to avoid a species that will get too large for your tank. The bushy nose pleco (Ancistrus sp.) stays small enough for a 10-gallon aquarium and makes a great companion for neon tetras.
The otocinclus is a smaller version of the larger pleco catfish. Like the pleco, they mostly eat algae and cling to the glass. However, in other ways they behave more like cory cats, preferring to live in schools and being more active during daylight hours. They are best kept in groups of at least six and do require some special feeding in the form of sinking algae wafers. Several species are available, but the most common is a black-and-white species
Ghost shrimp are a great "outside of the box" bottom feeder. Unlike everything else on the list, they are not fish, but small arthropods. They are often sold as live aquarium food, but will get along well in a small aquarium with small, peaceful fish like neon tetras. Their care is almost identical to the neon tetra, despite their wildly different appearance. They will actively scavenge for leftover food, eating it before it rots.