If you're really talking about GC4, then (a) only core worlds can build shipyards, and ( you build them as a planetary project (small button in the lower left corner of the planet window) not with constructors.  The structures are built by dragging an available improvement from the left part of the window to an available tile on the planet.

There's nothing on the left, though, that would let me build.

Is this a variant of #15 in https://forums.galciv4.com/510334/get;3838463 ? If so, just restart the game and the problem will go away.