I also did not get a single Code 19 for several weeks, but I fixed it about two weeks ago.
First place a large dinosaur (I selected a Sauropod) into your Asset Repository (to clear space).
Next go into your Asset Repository and place every single creature in your Asset Repository back into your park, one by one (I even opened each creature up when I did this, but I’m not certain this extra step was necessary).
When I placed my last remaining creature into the park this instantly triggered four or five Code 19’s in a row; confirming this method that I developed worked for me.
Afterwards I noticed that no more Code 19’s were popping for a few days, so I put one of every creature into the park (at least one Common, one Rare, one Super Rare, and one Legendary) and a few hours later another Code 19 popped… Now I get a couple of Code 19’s each day, so I’m pretty certain it’ll take either one of these two solutions (or both)