Cloning and genetic manipulation appear to be the Kaminoan's main export trade. The two primary canon factbooks (Star Wars: Absolutely Everything You Need to Know and Ultimate Star Wars) do offer some additional info about what they get up to when they're not making clone armies.
When they aren't making armies, the Kaminoans export clones for enforced slavery. They also develop exotic weaponry and (apparently) have something of a tourist trade, although this may be intended facetiously, given the planet's evident remoteness.
Kaminoans make precision tools and weapons
Underwater Tourism - Take a journey under the stormy seas in a
Star Wars: Absolutely Everything You Need to Know
Over the years, the Kaminoans developed cloning laboratories on their
homeworld and their clone creations began appearing on outlying world,
such as the mining planet of Subterrel.
Ultimate Star Wars
The (alas no longer canon) Inside the Worlds of Star Wars: Attack of the Clones and Star Wars: Attack of the Clones The Visual Dictionary factbooks also offer the following snippets of info.
Kamino is a remote and inhospitable world covered in one unending
ocean. Located in a dwarf satellite galaxy beyond the Outer Rim, the
planet receives very little traffic and only as much trade as is
necessary to supply the basic needs of its inhabitants, the amphibious
Kaminoans. This highly intelligent race has specialized in the
high-skill, value-added industry of human, alien, and creature
cloning, supplying a select client base with workers, private security
forces, and a range of unusual, one-off requests. The Kaminoans live
in stilt-cities scattered across the planet's watery surface, the
majority of which are devoted to cloning projects. The Kaminoans only
rarely receive visitors: The remoteness of the planet and its
extensive rainy season deters all but the occasional representative of
a clone purchasing authority.
Inside the Worlds of Star Wars: Attack of the Clones
When a global climate shift flooded their planet, the Kaminoans were
forced to adapt. They developed cloning technology and practised
selective breeding to keep their race alive. As a result of the
hardships endured during the Great Flood, the Kaminoans have an
austere, non-materialist outlook. They are outwardly polite, yet
behind this lurks an extreme intolerance of physical imperfection. The
Kaminoans are reliant on certain outworld technologies and raw
materials to maintain their advanced society, so they use their
cloning abilities to produce goods for export.
Star Wars: Attack of the Clones The Visual Dictionary