There are several raman active biomolecules. You need to find something that is in abundance in your sample. For tissue that contains hemoglobin, hemoglobin is very active if you shoot 405-420 nm light and the shifts are well known.
For visible light at low power look up the work by Matousek and McReery
if you want to perform quantitative analysis you have to find a functional group which vibrational band is in an undistributed range. (Raman is not sensitive to compounds it’s sensitive to functional groups (biomolecules contains C-C, C=O, C-N, OH, …).) If you perform the measurement in this way (try to use an internal standard) the critical point is the scattering cross-section. By comparing different bad you also have to consider the quantum yield of the detection unit (use the wavenumber which are similar to the one of the species you are interested in). The best way is to measure the spectra, analyse the composition and focus on a specific vibrational band e.g. C=Caromatic, C=O. Alternatively you can increase e.g. the C=O content by adding defined volumes of C=O containing species and calculate the C=O content without added compounds (be careful not to saturate the detection unit) . I suggest using a double bond vibrational band at around 1635 cm-1 (independent from ph).
You should probably focus on proteins, where you can work with the amide bands (amide I, II, III). Aromatic aminoacids like phenylalanine and tyrosine have sharp Raman peaks (around 850 and 1001 cm-1, respectively).
Also, lipids have several double bonds and C-H vibrations.
You could look up the chapter on biological molecules found in George Socrates' book: