If your ADC is taking 6 cycles to read at 300MHz clock rate, then your ADC interface sounds a bit strange.
I interface 1GHz dual-channel ADCs into Stratix II devices. The digitizers output 1Gbps signals which can be captured using the LVDS on the Stratix II. On a Stratix III you should be able to do something similar. I'm not sure what the LVDS limit on Cyclone III is.
However, it sounds like you are only wanting to sample a signal centered on 10MHz, and if you can really only read every 6th sample from your ADC operating at 300MHz, then your effective sampling frequency is only 300MHz/6 = 50MHz, so 25MHz is your Nyquist frequency.
Your external signal will need an analog filter that causes the signal amplitude to start to fall off at 10MHz (or whereever your signal is located) and by the time you get to 25MHz+15MHz = 40MHz, the signal power needs to be below your desired signal power at 10MHz (the signal at 40MHz will alias onto your signal at 10MHz when you sample at 25MHz).
Once the signal is sampled, and is inside the FPGA, you have to make sure you preserve the SNR you desire your signal to have though your digital processing, eg., you need to make sure you carry the right number of bits in your NCO and the output of your NCO.
The decimation rate you are considering 10MHz/100kHz is about 100x so you should be able to decimate using a multi-state design consisting of a CIC filter, followed by a pass-band cleanup filter (FIR or half-band). If you do not know these DSP terms, browse around MATLABs web. If you have a MATLAB license, you can use FDATool and the Filter Designer Toolbox to figure out what kind of filtering you need, then work your way through to an FPGA implementation.
If you don't have the tool then provide a clearer explanation of your design, and perhaps someone will provide an example design for you. For example, is the signal you are trying to demodulate at a fixed location? Can you change the ADC interface so that it can be run at 300MHz, if so, then your external filtering becomes simple, and you have more flexibility in your DSP code.
Cheers,
Dave