The following command, copied and pasted into a Terminal window, should install autokey:

sudo apt-get install autokey-gtk

Now I am no friend of the Software Center but the command line finds the package easily:

andrew@athens:~$ apt-cache search autokey
autokey-common - desktop automation utility - common data
autokey-gtk - desktop automation utility - GTK+ version
autokey-qt - desktop automation utility - KDE version
andrew@athens:~$ 

And trusty old Synaptic shows it clearly as well:

So perhaps follow my example and stick with these two :). The application installs fine from the command line on my Xenial installation:

Note: If testing this from a 'Live CD' you will need to enable the 'Universe' Repositories by following this path:

Dash --> Software & Updates --> Ubuntu Software

Then select the box 'Community-maintained free and open-source software (Universe).' Allow to reload and then install autokey-gtk as detailed previously...

References:

• Package: autokey-gtk (0.90.4-1) [universe]