The tree in Luke 17:6 is συκάμινος (sykaminos) in Greek. In Luke 19:4, however, another tree is named: συκομορέα (sykomorea).

Luther (and many others as well) nevertheless translated both as mulberry trees. This, however, does not make sense. If the text being translated distinguishes, two different trees will be meant.

The Old Testament, often the savior in such situations, unfortunately does not help here, for it uses only שִׁקְמָה (šiqmâ), which can mean both kinds of trees. The distinction whether in the Old Testament sometimes the mulberry tree and sometimes the mulberry fig is meant, must therefore be determined by the circumstances. For example, Amos (in Amos 7:14) will certainly not have gathered mulberry figs, because they do not taste as good as the fruit of the mulberry tree.

In my experience, the King James Bible translators have done a very accurate and good job on such points.

In the Old Testament, the King James Bible translates בָּכָא (bāḵā'; Strong's H1057) as "mulberry tree." Whereas שִׁקְמָה (šiqmâ; Strong's H8256) is translated as "sycomore trees." Finally, in Luke 17:6 "sycamine tree" (for συκάμινος, sykaminos, Strong's G4807) appears, whereas in Luke 19:4 "sycomore tree" is found (for συκομορέα, sykomorea, Strong's G4809).

Thus, for the correct German translation of all affected passages, the appropriate plant names must be found:

1. sycomore tree - lat. sycomore ficus moraceae -> mulberry fig, Adam's fig, donkey fig, sycomore.
   To make it easier to distinguish, donkey fig is a good choice, because these figs are hardly tasty.
   The would be correct in the following verses:
   Luke 19:4, Psalms 78:47, 1 Kings 10:27, Amos 7:14, 2 Chronicles 9:27, 2 Chronicles 1:15, 1 Chronicles 27:28.

2. sycamine tree - lat. morus nigra -> black mulberry
   The black mulberry yields the tasty fruit that resembles a blackberry.
   Only in Luke 17:6 is the black mulberry specifically mentioned.

3. mulberry tree - lat. morus (fam.) -> mulberry tree
   In general, the mulberry tree is mentioned in the following verses, without a more exact specification:
   2 Samuel 5:23, 1 Chronicles 14:4, 1 Chronicles 14:15, 2 Samuel 5:24.