Return an array which is iniated in a one liner

No line is required to return a c-array from a function, because you cannot return a c-array from a function.

You could dynamically allocate it and return a pointer to first element and size, but you better stay away from that in favor of std::array:

#include <array>

struct timeInDay {
  unsigned short hour;
  unsigned short minute;
};

std::array<timeInDay,1> getRingTimesForWeekDay(int day) {
  switch (day) {
    case 1:    return { {7, 50} };
    default:   return { {7, 50} };
  }
}

However, as others have mentioned already, the function does only return a single element, so it isnt clear why you want an array in the first place.

PS: If the size of the array is dynamic, use std::vector

Your getRingTimesForWeekDay just returns a timeInDay struct object. If you want to have an array of timeInDay structs, you can just define it:

[Demo]

    std::array<timeInDay, num_week_days> ringTimesForWeekDays{
        {{7, 50}, {7, 50}, {7, 20}, {7, 50}, {7, 50}, {7, 50}, {7, 50}}
    };

If you want to be able to regenerate the contents of the array by code later on, you can keep the getRingTimesForWeekDay function, and use it to fill the array:

[Demo]

    std::generate(std::begin(ringTimesForWeekDays), std::end(ringTimesForWeekDays),
        [d = DayOfWeek::MONDAY]() mutable {
            auto t{ getRingTimesForWeekDay(d) };
            d = static_cast<DayOfWeek>(static_cast<int>(d) + 1);
            return t;
        });

Also, you could initialize your array at compile time with the results of an immediately invoked lambda expression:

[Demo]

    constexpr auto ringTimesForWeekDays{
        [](){
            std::array<timeInDay, num_week_days> result{};

            std::generate(std::begin(result), std::end(result), [d = DayOfWeek::MONDAY]() mutable {
                    auto t{ getRingTimesForWeekDay(d) };
                    d = static_cast<DayOfWeek>(static_cast<int>(d) + 1);
                    return t;
                });

            return result;
        }()
    };