Weak entity with a many-to-many relationship with its owner
Yes, your entity is OK, but I would recommend this :


Do not use a multiple fields for your date. Instead of Day, Month, Year, you should use DateWorked. Maybe you are already doing that but it doesn't reflect in your explanations. This way, your date will always be valid. You won't have to check if February 30, 2013 is a valid date or not.
I strongly recommend using only 1 field surrogate primary key like HoursID. You can create a unique index on ConID and DateWorked to validate it will not exist more than once.
You may add complexity now or later by using ProjectID and that project could also bind to a ClientID.