I suggest the old work J. M. Barsom, Fatigue-Crack Propagation in Steels of Various Yield Strengths, Journal of Engineering for Industry 93(4):1190, DOI: 10.1115/1.3428061 (may be it have what you are looking for).

Generic C and m values can be seen at https://ocw.mit.edu/courses/materials-science-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/MIT3_11F99_fatigue.pdf

A "brief comment" on the topic:

Because of different processing and material specification, ..., be very careful with literature values for Paris law parameters C and m. Details to obtain these constants are covered by standards, but involve in general expensive testing.

Due to it, one may consider for design purposes in case of a lack of experimental fatigue data and as a first approximation, the useful way that is to estimate numerically (*) the parameter C as a function of the exponent m.

A relationship between C and m can be extracted from the onset of the Paris’ instability (Griffith-Irwin instability) and according to (*) is given by

C is approx = v_cr*[(1-R)*KIC]^(-m)

where v_cr is the (da/dN)at transition point between Region II and Region III, and R is the loading ratio (e.g. in stresses Smin/Smax). Both parameters v_cr and KIC can be known or estimated from materials with similar specification (composition, treatment and ...), e.g. from ASM handbook.

For details on the numerical estimation, see (*)M Mlikota et al 2017 J. Phys.: Conf. Ser. work. A two-scale approach, uses a micro-structure model (usually use FEM) to get the da/dN rate at crack tip e.g. based on Tanaka-Mura equation; and calculate stress intensity factor with a macro-scale model, and finally use the relationship between crack growth rate and the stress intensity to estimate C and m Paris law constants.

It is a recent subject and hope someone can add more information here.

The AFGROW software has a library including not only the Paris constants, but also the empirical constants of other fatigue crack growth models. The information is provided for various metallic alloys produced by different fabrication methods. In addition to the material constants, you may also perform the mentioned FCG analysis in that software and get the fatigue life as a result.

You can check the following web page to read more about it and get access to the software:

https://www.afgrow.net/

Good luck :)

If you have data for the material you are evaluating, I highly recommend calculating them yourself. It is very simple. Crude methods with crude are adequate: a log-log plot, a straight edge, and a calculator. Broek describes fitting the data in his book - The Practical Use of Fracture Mechanics. Fancy regression is more precision but probably not more accuracy.