NCBI provide interesting tools as the primer blast (https://www.ncbi.nlm.nih.gov/tools/primer-blast/). you'll just have to define the genome and run the soft.
I have done much sybr green qPCR; both in the cotext of standrad mRNA derived from tissues and cells and also miRNA derived from patient biopsy samples and plasmid
The issue with miRNA is often sensitivity of detection not anything specific about primer design for detection: Things like screning for stm loop and primer dimers ar pretty much standard whether you are looking at mRNA or miRNA
I have provided below some primer design rules that I use for making primers for both contexts and also an adapted pre amplification protocol in addition to RT which we tend to use when analysing vanashingly small quantities of miRNA from patient biopsy materials