Is there a way I can do the mordent that is shown in the pictures below in Sibelius? When I try to just put a sharp sign below the mordent, it doesn't play it correctly.
There is an Ornament Playback Plugin for Sibelius. You can select options for inverted and chromatic ornaments. Information about this plugin, including how to find it, can be found at this webpage.
UPDATE: the picture below shows where the Ornament Playback Plugin can be found in the Play tab of the ribbon (this is in the latest version, Sibelius 7):
The picture below shows the dialog box for the Ornament Playback Plugin, with the options that can be set:
The OP is absolutely right with his comments below. This plugin seems to have a bug. When you select Chromatic in General Options, the direction of the mordent is reversed: an upper mordent is played when Lower is selected; a lower mordent is played when Upper is selected. When the chromatic option is not selected the mordents play as expected. This is particularly annoying as the plugin adds the correct symbol for these chromatic mordents (although admittedly it doesn't add the accidental) even though the playback is wrong. So, for chromatic mordents, it is best to add the symbol manually, especially as you have to add the accidental anyway!