One way to do it would be to use the Access application itself to do the work. There is a DoCmd method, CopyObject, that will do exactly what you want. I tried the following code, and it worked (although it did, quite annoyingly, open the Northwind Database breifly on my computer before it shut it back down)
Private Sub Command3_Click()
Dim AccApp As Access.Application
Set AccApp = New Access.Application
AccApp.OpenCurrentDatabase "C:\Program Files\Microsoft Visual Studio\VB98\NWIND.MDB", False
AccApp.DoCmd.CopyObject "C:\Program Files\Microsoft Visual Studio\VB98\BIBLIO.MDB", "Employees2", acTable, "Employees"
AccApp.Quit acQuitSaveNone
That successfully copied the Employees table from the Northwind Database to the Biblio database, and named the table Employees2, complete with data. Except for that annoying flashing of Access opening breifly, it works great.
If the flashing of Access isn't acceptable, post back and we can think about it some more.