This is almost certainly blossom end rot (BER), a disorder that is usually caused by fluctuations in the plant's water supply, leading to a calcium deficiency. It affects a number of plants, including tomatoes, squash and eggplant. On peppers, the lesion is usually a tan color in the early stages, later turning brown or black, and can affect the side of the fruit, as in your first photo, as well as the blossom end.
You're right to water your plants thoroughly (superficial watering could cause them to surface-root, and become stressed), but once every two days may be over-frequent, unless, of course, the ambient temperature is very high, and the soil/compost is drying out very quickly; it should be slightly damp most of the time, not wet. Over-watering washes calcium out of the soil and is another cause of BER.
You will find detailed information/links about BER and steps you can take to control it, in my answer to a similar question here. There is also a good overview of the problem here