From basic knowledge of analytical chemistry, you could adsorb your sample on a rough gold or silver substrate and then use surface enhanced Raman Spectroscopy to probe your sample.
You do not give away much details on the materials and Raman system you are working with so my answer can only be general.
Patience is usually the fastest way. Doing a measurement of a couple of hours is usually a much quicker solution than changing your Raman set up or changing to SERS. Getting SERS to work may also take a few days.
Consider that Raman is a linear process so the signal you get increases with time and laser power and so the S/N ratio improves over time (Noise = square root of the signal when shot noise limited). There are a few things you have to take into account though: Your detector introduces two types of noise that you have to take into account: Read out noise (so minimize the number of acculuations) and dark current (minimize the detector temperature to reduce that). The detection limit of your system can be calculated from the dark noise and read out noise characteristics. If you have fluorescence issues than this background contributes in the form of shot-noise.
Fluorescende may or may not be bleached away. Changing excitaion wavelength may help but I do not know if you have that option.
I agree with Rolf. One small tip; I dont know if you are conducting your experiment in a black box or not. If not, then stray light in the room could increase the background signal and thus decrease your S/N considerably. I was facing this problem with my fluorescence lifetime experiments. Temporarily, I made a box out of black cardboard and covered my emission pathway. This way, stray light was reduced considerably and my noise was reduced by 40 times. Hope it helps in some way. Good luck!
I am looking for analysis in liquid state only and do not intend to perform SERS. Have been performing the experiment over hydrophobic surfaces to hold the liquid drop (10 µl) intact. However, I am wondering if any additive or special substrate could yeild a better signal in liquid state itself. The experiment is being carried out inside a dark chamber only. Also, I would like to know if NIR laser would be a better choice than 532 nm laser for such kind of analyis.
Again, a very general answer: Performing Raman in the NIR region makes sense if your sample doesn't fluoresce in the NIR region. Thereby, you reduce the fluorescence noise. However, photons of NIR light have lesser energy than the VIS light, and to reduce dark current you are cooling your detector, the efficiency of the experiment suffers resulting into higher data acquisition time. That will be my guess.
For comparison people do Raman on blood sugar in the mM range ~ 300-700 mg/ml. Blood is a difficult substance to find anything in but you are 30 to 300 times lower in concentration. You picked yourself a challenge!
There are two ways that you could try to enhance the signal in the liquid phase (a) UVRR (b) using PCF. There is no problem to measure down to mM range directly in the liquid state. I would doubt if Raman could reach down to 10-5 at all if you don't want to use colloidal nanoparticle solution to enhance the signal.