We have used the TaqMan SNP Genotyping Assays (Applied Biosystems/Life Technologies, Grand Island, NY, USA). Primers are designed using the Custom TaqMan Assay Design Tool (https://www.lifetechnologies.com/order/custom-genomic-products/tools/genotyping/). PUblication pending revsions and second review.
I may misunderstand your question. You can definitely design primers to specifically amplify the region of interest with 1 SNP. Is that what you want to know?
Actually, if you design primers and do a High Resolution Melting (HRM) analysis of the complex using SYBR green assay using platform like illumina, its possible to look for the SNPs. This is one way of doing it and HRM will do it efficiently.
If you know the SNP, you can just add a matching base at the 3'-end of the primer. This primer will work with the wild type template too but with a slightly higher Ct value (RealTime-PCR). Whether or not this primer makes non-specificity product generation is a question which have an answer as: dependent on template sequence and other primer. Check the self- and hetero-dimers of the designed sequences using the link provided below. If there is no dimer lower than -6kcal/mole you can proceed. Also, try AT-rich 3'-end which helps reduce non-specific binding at lower annealing temperatures. Try a longmer with annealing temperature close to Tm. This would significantly reduce non-specificity and broaden the gap between the Ct s from wild type and mutant type amplification. Hope this helps.
Another option is to use a molecular beacon - a dual-labeled probe held in hairpin loop that opens and fluoresces when it binds its target. The beacons can be expensive and need to be carefully designed but can be tested for nonspecific binding. I designed some to differentiate 2 very similar RNA species and got non-specific less than 1%. also the beacons detect to very low levels of target cDNA - i got detection at attogram levels on my standard curve.
original paper, that states use for SNP differentiation