If the gene is already cloned in a plasmid, design outward-facing PCR primers from the deletion boundaries, then PCR with Phusion or any other high processivity proofreading polymerase, digest with Dpn I to get rid of the template (make sure the original DNA was propagated in a dam+ strain), phosphorylate with PNK (or, if you incorporated a silent restriction site, digest with the relevant enzyme), ligate and transform.
The best is to clone your gene of interest inside a plasmid . I have done several deletion of 50 bp to 250 bp inside a promoter inserted into a plasmid with Q5 site-directed mutagenesis kit from NEB . NEB have also a tool in the website to help you to create your primer to do the reaction . I think the principe of this kit is very similar to the previous answer :)
Chemical synthesis with defined deletion is the most reliable method. The synthesis is affordable these days.
Pick two conveniently located, ideally unique, restriction sites flanking the target deletion region, get the piece of DNA extending slightly beyond restriction sites on both sides synthesized, cut the synthetic DNA with restriction enzymes and ligate into the cloned gene with the wild version od the same region removed.