WineHQ on Ubuntu 19.10
Solution 1:
does not have a release file
indicate the repository has no support for your Ubuntu release, in this case it's Ubuntu Eoan → 19.10.
You have added deprecated/outdated repository, the developer has put up an announcement regarding this issue on the WineHQ mailing list https://www.winehq.org/pipermail/wine-devel/2017-March/117104.html.
You have to follow the new guide for installing Wine, luckily the Wine team has made this easy by posting a complete guide on their site— which you can uses with your 19.10.
sudo dpkg --add-architecture i386
wget -nc -qO- https://dl.winehq.org/wine-builds/winehq.key | sudo apt-key add -
sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/ eoan main'
Then install the packages.
sudo apt install --install-recommends winehq-staging
According to https://dl.winehq.org/wine-builds/ubuntu/dists/eoan/main/binary-amd64/, the only available version is: staging
and devel
UPDATE
The new repo works fine, it's just you haven't removed old obsolete repo which you added before.
sudo add-apt-repository --remove ppa:wine/wine-builds
sudo apt update
Now there should not be any error.
Solution 2:
My solution for 19.10; (It's worked for me on Ubuntu 19.10)
Don't use this repository:
sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/ eoan main'
Use this repository:
sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/bionic main'
"eoan main" is recommented by winehq official website but not works. If you trying using 19.04 repository on 19.10, its works fine :)
If you want to use WineHQ for 19.10, enter this commands;
(Switch to "root" user.)
sudo dpkg --add-architecture i386
wget -nc https://dl.winehq.org/wine-builds/winehq.key
sudo apt-key add winehq.key
rm -rf winehq.key
sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/ disco main'
sudo apt update
sudo apt install --install-recommends winehq-stable
For testing, enter this command:
winecfg