Universal　computation　of　a　quantum　system　consisting　of　superpositions　of　well-separated　coherent　states　of　multiple　harmonic　oscillators　can　be　achieved　by　three　families　of　adiabatic　holonomic　gates.　The　first　gate　consists　of　moving　a　coherent　state　around　a　closed　path　in　phase　space,　resulting　in　a　relative　Berry　phase　between　that　state　and　the　other　states.　The　second　gate　consists　of　＂colliding＂　two　coherent　states　of　the　same　oscillator,　resulting　in　coherent　population　transfer　between　them.　The　third　gate　is　an　effective　controlled-phase　gate　on　coherent　states　of　two　different　oscillators.　Such　gates　should　be　realizable　via　reservoir　engineering　of　systems　that　support　tunable　nonlinearities,　such　as　trapped　ions　and　circuit　QED.