Well I found a solution in the meantime (thanks to the folks at vbdotnetformums.com, so I would like to share the results:
First possible solution could be defining the parameter as Object and default value as Nothing. Then Cast the DateTime.
Second and cleaner solution (and the one I followed) was to overload the constructor.
Here is the solution by IanRyder (vbdotnetforums.com):
Public Class MyClassExample
Public Property DateToUseInClass As DateTime
Public Sub New()
DateToUseInClass = System.DateTime.Now
End Sub
Public Sub New(ByVal GivenDate As System.DateTime)
DateToUseInClass = GivenDate
End Sub
End Class
Then I can realise the behavior I wanted to have:
Dim myVariable As New MyClassExample
Dim myVariable As New MyClassExample(DateTime.Today.AddDays(-1))
It worked exactly the way I wanted it. I hope someone else will profit from it some day.