Edit in JSFiddle

/*
 * カレンダー設定
 *
 * monthOffset:     カレンダーを生成する月（yyyy/mm）
 * publicHolidays:  祝日
 */
const CALENDAR_SETTINGS = [
    {
        monthOffset:     '2019/12',
        publicHolidays:  [],
    },
    {
        monthOffset:     '2020/01',
        publicHolidays:  [1, 13],
    },
];

$(window).on('load', function() {
    // 営業日カレンダーを出力
    $.each(CALENDAR_SETTINGS, function(index, settings) {
        rendarCalendar(settings);
    });
});

/**
 * カレンダーを出力する
 *
 * @param object settigs 設定オブジェクト
 * @return void
 */
function rendarCalendar(settings) {
    const weekLabels = ['日', '月', '火', '水', '木', '金', '土'];
    const classes = {
        container: 'p-calendars__container',
        table: 'c-calendar',
        caption: 'c-calendar__caption',
        today: 'c-calendar__today',
        sunday: 'c-calendar__sunday',
        saturday: 'c-calendar__saturday',
        publicholidays: 'c-calendar__public-holidays',
    }

    const today = new Date();
    const monthOffset = settings.monthOffset ? new Date(settings.monthOffset + '/01') : today;
    const currentYear = monthOffset.getFullYear();
    const currentMonth = monthOffset.getMonth();
    const firstDay = new Date(currentYear, currentMonth, 1);
    const nextMonth = new Date(currentYear, firstDay.getMonth() + 1).getMonth();

    const year = firstDay.getFullYear();
    const month = firstDay.getMonth();
    const day = new Date(year, month, firstDay.getDate() - firstDay.getDay());

    const calendars = $('.p-calendars');
    const calendar_container = $('<div>').addClass(classes.container);
    const calendar = $('<table>').addClass(classes.table);
    const caption = $('<caption>').addClass(classes.caption);

    appendCaption();
    appendWeeks();
    appendBody();

    calendars.append(calendar_container.append(calendar));

    /**
     * キャプション（年月）と追加する
     *
     * @return void
     */
    function appendCaption() {
        caption.append(year + '年 ' + (month + 1) + '月');
        calendar.append(caption);
    }

    /**
     * 曜日を追加する
     *
     * @return void
     */
    function appendWeeks() {
        const thead = $('<thead>');
        const weeks = $('<tr>');

        $.each(weekLabels, function(index, value) {
            const th = $('<th>' + value + '</th>').attr('scope','col');

            // 日曜日
            if (index === 0) {
                th.addClass(classes.cellSunday);

            // 土曜日
            } else if (index === 6) {
                th.addClass(classes.cellSaturday);
            }

            weeks.append(th);
        });

        thead.append(weeks)
        calendar.append(thead);
    }

    /**
     * 日付を追加する
     *
     * @return void
     */
    function appendBody() {
        const tbody = $('<tbody>');

        for (let row = 0; row < 10; row++) {
            const daysLine = $('<tr>');

            for(let col = 0; col < 7; col++) {
                const td = $('<td>');

                if (day.getMonth() === month) {
                    td.text(day.getDate());

                    // 当日
                    if (isSameDate(day, today)) {
                        td.addClass(classes.today);
                    }

                    // 日曜日
                    if (day.getDay() === 0) {
                        td.addClass(classes.sunday);

                    // 祝日
                    } else if ($.inArray(day.getDate(), settings.publicHolidays) !== -1) {
                        td.addClass(classes.publicholidays);

                    // 土曜日
                    } else if (day.getDay() === 6) {
                        td.addClass(classes.saturday);
                    }

                } else {
                    td.html('&nbsp;');
                }

                daysLine.append(td);

                day.setDate(day.getDate() + 1);
            }

            tbody.append(daysLine)

            if (day.getMonth() === nextMonth) break;
        }

        calendar.append(tbody);
    }

    /**
     * 2つの年月日が同じかを返す
     *
     * @param Date date1
     * @param Date.date2
     * @return bool
     */
     function isSameDate(date1, date2) {
        if (
            date1.getFullYear() === date2.getFullYear()
                && date1.getMonth() === date2.getMonth()
                && date1.getDate() === date2.getDate()
        ) {
            return true;
        }

        return false;
     }
}

<div class="p-calendars"></div>

.p-calendars {
    max-width: 200px;
    
    > *:nth-child(n+2) {
        margin-top: 20px;
    }
}

.c-calendar {
    table-layout: fixed;
    border-collapse: collapse;
    width: 100%;

    th, td {
        vertical-align: middle;
        text-align: center;
        line-height: 1.75;
    }

    &__caption {
        margin-bottom: 5px;
        padding-bottom: 5px;
        border-bottom: 1px solid #ccc;
        font-weight: 700;
    }

    &__today {
        font-weight: 700;
    }

    &__sunday {
        color: #f00;
    }

    &__saturday {
        color: #00f;
    }

    &__public-holidays {
        color: #f00;
    }
}