java.time
The java.util Date-Time API and their formatting API, SimpleDateFormat are outdated and error-prone. It is recommended to stop using them completely and switch to the modern Date-Time API*.
Also, quoted below is a notice from the home page of Joda-Time:
Note that from Java SE 8 onwards, users are asked to migrate to java.time (JSR-310) - a core part of the JDK which replaces this project.
Solution using java.time, the modern Date-Time API:
List<LocalDate> getDateList(int year, String monthname) {
    int month = Month.valueOf(monthname.toUpperCase()).getValue();
    
    return IntStream
            .rangeClosed(1, YearMonth.of(year, month).lengthOfMonth())
            .mapToObj(i -> LocalDate.of(year, month, i))
            .collect(Collectors.toList());
}
Demo:
import java.time.LocalDate;
import java.time.Month;
import java.time.YearMonth;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
public class Main {
    public static void main(String[] args) {
        // Test
        getDateList(2017, "February").forEach(System.out::println);
        System.out.println("=*==*==*=*=");
        getDateList(2016, "February").forEach(System.out::println);
    }
    static List<LocalDate> getDateList(int year, String monthname) {
        int month = Month.valueOf(monthname.toUpperCase()).getValue();
        
        return IntStream
                .rangeClosed(1, YearMonth.of(year, month).lengthOfMonth())
                .mapToObj(i -> LocalDate.of(year, month, i))
                .collect(Collectors.toList());
    }
}
Output:
2017-02-01
2017-02-02
...
...
...
2017-02-27
2017-02-28
=*==*==*=*=
2016-02-01
2016-02-02
...
...
...
2016-02-28
2016-02-29
ONLINE DEMO
Learn more about the modern Date-Time API from Trail: Date Time.
* For any reason, if you have to stick to Java 6 or Java 7, you can use ThreeTen-Backport which backports most of the java.time functionality to Java 6 & 7. If you are working for an Android project and your Android API level is still not compliant with Java-8, check Java 8+ APIs available through desugaring and How to use ThreeTenABP in Android Project.