When I first looked for tires for my 41 Master Deluxe the issue I found was finding tires thin enough to fit the rim.  I could not find tires tall enough but none that would fit a rim that narrow.  I ended up buying a used set of the original size.  

Here is a link to a thread I found on the old site for a similar topic:

https://vccachat.org/ubbthreads.php/topics/379233/tire-size-for-a-1941-chevrolet.html

@timothy-kruger TY.......

Meant to say I could find them tall enough and not wide enough.  FYI I had an issue finding raised white letter tires the right size for my 87 Monte Carlo LS.  And that is a much more recent car.  

Based on section width and overall diameter I found that a 185/85x16 would be a close substitution for the 600x16 as far as size goes. Assuming the 600 is 6" wide an actual exact replacement width wise would be a 152mm wide tire rather than the 185 but no one makes a 150mm wide tire that I'm aware of. If they did the profile would have to be a 95 or so to get the desired diameter. The issue back then (I think still today but haven't checked lately) is that 185s aren't sold in the US. One would have to buy a set in Europe and have them sent over. It would be cheaper to just buy Coker's 600Rx16 tires. Diamondback also sells a 600Rx16 tire if you're not sold on Coker.

@tiny How about a modern set of 215 70R 16's.for 4" rims?

I think 215 would be too wide for a 4" rim, I would not go over 165 which is a good width for 4 1/2" or 5" rim.  I will need to go shopping in the future but I know my rims need major work and may get them widened to suit a more readily available tire when the time comes. I run 195 14 on 5 1/2" rims for my daily driver.

Tony

That's a pretty wide tire for a 4" rim. I don't know if it would be mountable or not. IMHO it wouldn't look right, it would look like a size 10 body stuffed into size 6 pants. Doing a search I see 185/85Rx16s are now being sold in the US. If I was buying for my vehicle and wanted the modern tire look that's the way I'd go. They are a bit wider than a 600 but not enough to look funny. Not making a recommendation, just my opinion.

@tiny TY Tiny, for your help.