There is no way to turn coins into bux.
Coins are easy to come by. The player accumulates coins automatically, as long as the player has any actual residents. Stocking levels that sell items just permits a player to earn coins faster.
Bux are the special currency that allows you to speed up tasks, buy special items, upgrade how much stock a store can hold any time the player desires, move a level any time desired, get a cash bonus immediately by selling all of an item in stock, or pick a specific level in Tiny Death Star. This is a nudge to players to give the developer money in return for many buxs so the player can do more things in TDS more quickly.