205 nm UV-Vis readings
This may be what you are looking for. The conversion formula is:

$$
\text{Protein concentration (mg/ml)} = \frac{ (\text{Absorbance at 205 nm})} {31}
$$

The first, Scopes, does indicate that nucleic acid contaminants will confounding 205 nm absorbance readings. It seems as though this spetrophotometic calculation is feasible for relatively pure protein species.