Why can't I install Tomboy in Ubuntu Mate 19.04?

Tomboy has been discontinued in Ubuntu 19.04 and later, however Gnote is almost identical to Tomboy and in fact you can export Tomboy notes and then copy all of them together into Gnote. You can also export Gnote notes and then copy all of them together into Tomboy. You can use Gnote as a backup app to store backups of Tomboy notes and vice versa, because Tomboy notes and Gnote notes are completely compatible.

To install Gnote open the terminal and type:

sudo apt install gnote  

Please examine your link to packages.ubuntu.com more closely: The TomBoy package is available in Cosmic, but not Disco.

Looking further into the problem:

Tomboy is a gnome application, and can be found at https://wiki.gnome.org/Apps/Tomboy. Following the links to the github, it seems that Tomboy 1.15 is the latest version and has not been updated since 2017. You could download and compile this yourself. I assume that this does not work well, or the Ubuntu developers would have included it in the Disco release.

There is also Tomboy-ng, the current development branch of Tomboy at version 0.21. The github has links for .deb files, and instructions for installation, at https://wiki.gnome.org/Apps/Tomboy/tomboy-ng/DownLoadInstall

As per Tomboy's website, the package tomboy is no longer maintained. A new project was started called tomboy-ng. This package is not available in Ubuntu's repositories, but you can download it from the git-website. The instructions for downloading and installing tomboy-ng are on their website as well.