In general, it is not advisable to use Derby Embedded database for persistent EJB timers due to limitations of Derby Embedded that all connections use the same class loader (implying the same JVM as well). This means you cannot leverage the failover capability (missedTaskThreshold setting) or even have multiple servers connected to the database at all. If you decide to use a Derby Embedded database, it means that you are limiting yourself to a single server. You can decide for yourself if that is acceptable based on what your needs are.
In the case of the example configuration you gave, it doesn't work because the EJB persistent timers feature in Liberty has no way of knowing that you dataSource, "DefaultDerbyDatasource" with jndiName "jdbc/defaultDatasource" is the data source that it ought to use. Also, it is incorrect to specify transactional="false" on the data source that you want EJB persistent timers to use because EJB persistent timers are transactional in nature.
I assume that what you are intending to do is configure the Java EE default data source and expecting EJB persistent timers to use it. That approach will work, except that you'll need to configure the Java EE default data source, you need to specify the id as "DefaultDataSource".
Here is an example that switches your configured data source to the Java EE default data source and removes the transactional="false" config,
<library id="DerbyLib">
<fileset dir="/tmp/derby/lib" includes="derby.jar"/>
</library>
<dataSource id="DefaultDataSource" jndiName="jdbc/defaultDatasource" statementCacheSize="10">
<jdbcDriver libraryRef="DerbyLib"/>
<properties.derby.embedded createDatabase="create" databaseName="/tmp/sample.ejbtimer.db" shutdownDatabase="false"/>
<containerAuthData user="user1" password="derbyuser" />
</dataSource>
By default, the EJB persistent timers feature should create database tables once the application runs and the EJB module is used.
However, you may be able to verify the configuration prior to that point by running the ddlgen utility (after correcting the configuration as above)
https://www.ibm.com/docs/en/was-liberty/base?topic=line-running-ddlgen-utility
which gives you the opportunity to see the DDL that it will use and optionally to run it manually (which is useful if you turned off automatic table creation via
<databaseStore id="defaultDatabaseStore" createTables="false"/>
)