(Tested with KeePassXC on Fedora 25)
By default when using GNOME Keyring you have a keyring that is unlocked when you log in (usually called "Login"). You can make use of that by storing a KeePass database password in this keyring and using it to automatically unlock your KeePass database.
Store the KeePass database password in GNOME Keyring. You'll have to set a label and at least one attribute/value pair. The label is displayed in a GNOME keyring manager (e.g. Seahorse), the attribute/value pair should be a unique identifier because it's needed for the lookup. I suggest to use keepass as attribute and the database name as value (make sure it doesn't contain any spaces).
secret-tool store --label="KeePass <database_name>" keepass <database_name>
Then create a script to launch and immediately unlock your KeePass database.