(1) Background: A premature termination codon (PTC) can be induced by a type of point mutation known as a nonsense mutation, which occurs within the coding region. Approximately 3.8% of human cancer patients have nonsense mutations of p53. However, the non-aminoglycoside drug PTC124 has shown potential to promote PTC readthrough and rescue full-length proteins. The COSMIC database contains 201 types of p53 nonsense mutations in cancers. We built a simple and affordable method to create different nonsense mutation clones of p53 for the study of the PTC readthrough activity of PTC124. (2) Methods: A modified inverse PCR-based site-directed mutagenesis method was used to clone the four nonsense mutations of p53, including W91X, S94X, R306X, and R342X. Each clone was transfected into p53 null H1299 cells and then treated with 50 μM of PTC124. (3) Results: PTC124 induced p53 re-expression in H1299-R306X and H1299-R342X clones but not in H1299-W91X and H1299-S94X clones. (4) Conclusions: Our data showed that PTC124 more effectively rescued the C-terminal of p53 nonsense mutations than the N-terminal of p53 nonsense mutations. We introduced a fast and low-cost site-directed mutagenesis method to clone the different nonsense mutations of p53 for drug screening.