Edward Mills writes:

The 15 in tires in the sizes we would see on big 50's-60's Chryslers would have typically been 7.60-15 or 8.00-15. These translate roughly to P225/75R15 and P235/75R15. Because these are lower profile (75 series = Height of cross section is 75% of cross section Width) vs original tires which were 83 series (83%), these tires are typically shorter overall - for example a 7.60-15 was typically 28.7 in to 29 in Overall diameter. The 8.00-15 was 29.3 to 29.7 in OD.
The 7.60-15 was rated at 1225 lb at 24 psi or 1310 lb at 26 psi. The 8.00-15 were rated at 1335 at 24 or 1395 at 26 psi. These were the 4 ply standard OE tires. Station Wagons and some High Performance ran 6 ply with higher load capacity at higher pressures.
Yes Manufacturers wanted a soft ride back then - owners manuals frequently recommended 4 psi higher pressure with full load (5 passengers and some luggage) OR at high speed (Interstates 70 mph considered high) - we typically recommended and ran 32 psi.
The P225/75R15 is typically 28.05 in OD (Cooper Trendsetter) to 28.3 in (Hankook), while the P235/75R15 is typically 28.65 (Cooper) to 28.9 in OD. Hence the P235/75R15 (28.65-28.9 in OD) is a closer match to dimensions of the 7.60-15 (28.7-29 in OD).
The P225/75R15 (102 Load Range) are typically rated at 1885 lb at 44 psi and the P235/75R15 (105 Load Range) are typically rated at 2028 lb at 44 psi. There are also P235/75R15 XL (Extra Load) (108 or 109 Load Range) that are rated to 2183 or 2271 lb respectively.
So my bottom line is go to the P235/75R15 as best option. It provides the tallest tire commonly available (not perfect, but nearest match to ride height) and there are a lot more options in this size as it was used on many pickup trucks. As to load capacity, the standard 105 Load Range should be more than sufficient. If you really want the max load capacity, go to the XL variants - BUT STAY AWAY FROM the LT235/75R15 - it offers more load capacity but at a significantly stiffer ride (it may rattle your bones - I went that way on a Jeep and regretted it.)
If you want to go 70 series, a P235/70R15 (27.9 in OD) is loadwise equivalent to the smaller P225/75R15, but you are compromising geometry (and speedometer error) compared to the P235/75R15.

Now as to 14's we are pretty much out of luck replacing an 8.50-14 or a 9.00-14. The biggest 14 inch mass produced tire I found last time I did the research was a P215/75R14 (roughly same as P225/70R14).
As to the P215/75R14, there are a few name brand options including some Narrow Whitewalls. They are the evolution of the 8.00-14 (to 8.25-14 to G78-14 or G70-14 to 215/75R14). However the P215/75R14 (27.0 in OD, Load Range 98, 1664 lb load at 44 psi) is significantly smaller than the 8.50-14 (28.1-28.4 in OD, 1265 lb at 24 psi) or the 9.00-14 (28.7-29.0 in OD, 1355 lb at 24 psi). They may handle the load OK, but you sacrifice ride height.
There used to be some production grade P225/75R14 and P235/75R14 but the last Coopers went away around 2006 leaving only the Specialty tires = Coker or American Classic in the P235/75R14. Diamond Back also has a nice looking Auburn Classic in the HR78-14 (equivalent to 8.50-14 or P225/75R14 - 27.5 in OD) which looks almost identical to the HR78-14 Michelin X Radial of the 1970's.
But personally I try to avoid Specialty tires (especially the bias reproductions) as they are typically made in small batches using older technology and manual labor which may result in more variability that current Production grade tires using automated equipment. They are also significantly more expensive. But as I said previously - I would stay with a name I recognize and avoid tires made in China. As to Load Range Suffixes, you will mostly find S or T - written Load Range 102T or 105T or 102S etc. H, V, W, Y, Z are all high speed ant you are unlikely to encounter those in 14 or 15 inch offerings. But stay away from lower letters in the alphabet before S, like N or Q (except H).
One last WARNING - STAY AWAY FROM tires with the letters "ST" written as part of the size designation - these are designed for Trailer Use Only at relatively low speeds some as low as 55 mph as I recall.