The best way to find a pair of primers is through use bioinformatics tools. There are some bioinformatic tools that can be used on line and others like desktop software. In the first set I recommend primer-BLAST (http://www.ncbi.nlm.nih.gov/tools/primer-blast/), where having the fasta sequence of interest is possible to specify in which regions of the sequence you want to design primers. I also recommend the free online tool called Benchling. Furthermore, the vector NTI software, by Applied Biosystems is very robust, but it is not free. It is posible to obatain the Fasta beta-globulin gene sequence in databases like Genome Browser (https://genome.ucsc.edu/cgi-bin/hgGateway), Map Viewer (http://www.ncbi.nlm.nih.gov/genome/guide/human/) and Ensembl (http://www.ensembl.org/index.html).
Here are the beta globin gene primer sequences for forward and reverse primers, which are we using in our lab as an internal control for diagnosis of other human gene mutations.
Forward : - "GAA GAG CCA AGG ACA GGT AC" 20 nT.
Reverse : - "CAA CTT CAT CCA CGT TAC ACC" 21 nT.
these primers will work good at following cycling condition.
95 degree for 5 min.
95 D C for 1min, 55 D C for 2 min, 72 D C for 1 Min X 35 Cycle
72 D C for 4 min.
These will give you the 268 base pair product on agarose gel.
You can also check these primers on PRIMER3 software available free on google by adding sequence of beta globin gene freom NCBI.