Psundstrom58,
I wonder how your radio project turned out? I meant to send a post about it at the time. Well, does your set have individual coils for the (4) bands? That is, does it have (4) antenna coils and (4) oscillator coils for the 6K8 converter stage? Some of these sets had all the antenna coils for the various bands wound on one long coil form. Same for the oscillator coils as well so that is why I ask. They did this to save money on low cost beginner sets. If it has individual antenna coils then you could use just about any broadcast band antenna coil from a parts set as a replacement that will fit. It sounds like that is the case from you posting. Replacement antenna coils that have an adjustable iron or ferrite core are especially good replacements as you can dial those in to track well with the tuning capacitor and the 6K8 oscillator stage in your set.
The alignment procedure for the new antenna coil will be to adjust the core in it (if present) at the low end of the BC band (600 kHz) and the antenna trimmer for the BC band at the high end (1400 kHz). The trimmer capacitor may be part of a row of (4) such adjustable mica capacitors. You'll need a signal generator or you could tune around for a BC station of approximately these frequencies for the signal source. The signal generator is preferred as the receiver's sensitivity may be way down at first with the new antenna coil in place. Adjust the coil and trimmer for maximum output at these (2) frequencies. Then repeat this procedure a few times until you can't get any more improvement in output.
New antenna coils can be bought from Antique Electronic Supply for the broadcast band. eBay seller listings will be another source for NOS Miller, Meissner, Merit and other coil manufacturer's antenna coils. Of course, you could look around for a parts set as well. I am thinking that the coils out of a Hallicrafters S-38 might be suitable as it is a similar set to the S-19R. Good luck.