Cardiac rehabilitation (CR) is recommended after myocardial infarction (MI) or heart failure (HF), yet the added value of core muscle endurance training within CR remains uncertain. This randomized, three-arm trial will enroll 60 adults with stable MI or HF who are referred to Phase II CR. After consent and baseline testing, participants are allocated 1:1:1 to: (1) Pilates-based core endurance training, (2) standard aerobic CR (treadmill or cycle), or (3) combined aerobic plus core training. Supervised sessions occur twice weekly for eight weeks (\~60 minutes/session) with continuous safety monitoring. The primary aim is to evaluate feasibility and safety of core training in this population. The study also compares effects of the three programs on cardiorespiratory fitness and function (e.g., peak oxygen uptake, six-minute walk distance), core endurance, balance, symptoms, and health-related quality of life. Findings will clarify whether adding core training improves outcomes and inform clinical exercise prescription in CR.