[Arran]

Mike;
The watch batteries will fit the original bias cell holder, if you choose one of the correct diameter. The positive of the watch/coin cell will fit flat against the edge of the cylindrical part of the bias cell holder (which is what Rogers and apparently this Philco 37-604 used) and the spring contact will press against the negative part at the center of the watch cell. again the Mallory bias cells had the polarity the opposite way around from a modern watch battery/cell so you would need to flip the connection to make it work. There is another type of bias cell holder that is made out of stiff piece of wire, and I'm not sure if those would fit a watch battery like the type the Rogers sets used with the cylinder, they look like a stupid design anyhow.
Here is some history behind the Mallory bias cells:
https://antiquewireless.org/wp-content/u...s_cell.pdf
Also here: https://antiqradio.com/post_mallory-bias-cells.html
Another method is to hollow out the old cell and use it as an adapter for the new watch battery, like they did on this thread, he used an LR44: https://www.vintage-radio.net/forum/show...?p=1386709
As I mentioned before Rogers and Canadian Marconi really took a shine to these infernal things, and I guess that the engineers behind the Philco 37-604 did as well, so radio collectors in Canada are quite familiar with them. When they go dead the radio basically stops working as well, I think that the cost savings in parts was not the motivation since you need the holder as well as the cell (something not mentioned in the advertising) as opposed to a resistor and bypass capacitor on the tube cathode.
Regards
Arran