Sorry, it is not supported. It seems that days and years are the only thing that supports min and max. It is probably not difficult to add to the code if you unlock its repo.
You can see all the parameters, documented and undocumented, by looking at the source on github https://github.com/jtsage/jquery-mobile-datebox/blob/master/js/jquery.mobile.datebox.js
options: { // All widget options, including some internal runtime details version: '1.0.1-2012022700', // jQMMajor.jQMMinor.DBoxMinor-YrMoDaySerial theme: false, defaultTheme: 'c', pickPageTheme: 'b', pickPageInputTheme: 'e', pickPageButtonTheme: 'a', pickPageHighButtonTheme: 'e', pickPageOHighButtonTheme: 'e', pickPageOAHighButtonTheme: 'e', pickPageODHighButtonTheme: 'e', pickPageTodayButtonTheme: 'e', pickPageSlideButtonTheme: 'd', pickPageFlipButtonTheme: 'b', forceInheritTheme: false, centerWindow: false, calHighToday: true, calHighPicked: true, transition: 'pop', noAnimation: false, disableManualInput: false, disabled: false, wheelExists: false, swipeEnabled: true, zindex: '500', debug: false, clickEvent: 'vclick', numberInputEnhance: true, internalInputType: 'text', resizeListener: true, titleDialogLabel: false, meridiemLetters: ['AM', 'PM'], timeOutputOverride: false, timeFormats: { '12': '%l:%M %p', '24': '%k:%M' }, durationFormat: 'DD ddd, hh:ii:ss', timeOutput: false, rolloverMode: { 'm': true, 'd': true, 'h': true, 'i': true, 's': true }, mode: 'datebox', calShowDays: true, calShowOnlyMonth: false, useDialogForceTrue: false, useDialogForceFalse: true, fullScreen: false, fullScreenAlways: false, useDialog: false, useModal: false, useInline: false, useInlineBlind: false, useClearButton: false, collapseButtons: false, noButtonFocusMode: false, focusMode: false, noButton: false, noSetButton: false, openCallback: false, openCallbackArgs: [], closeCallback: false, closeCallbackArgs: [], open: false, nestedBox: false, lastDuration: false, fieldsOrder: false, fieldsOrderOverride: false, durationOrder: ['d', 'h', 'i', 's'], defaultDateFormat: '%Y-%m-%d', dateFormat: false, timeFormatOverride: false, headerFormat: false, dateOutput: false, minuteStep: 1, calTodayButton: false, calWeekMode: false, calWeekModeFirstDay: 1, calWeekModeHighlight: true, calStartDay: false, defaultPickerValue: false, defaultDate : false, //this is deprecated and will be removed in the future versions (ok, may be not) minYear: false, maxYear: false, afterToday: false, beforeToday: false, maxDays: false, minDays: false, highDays: false, highDates: false, highDatesAlt: false, blackDays: false, blackDates: false, enableDates: false, fixDateArrays: false, durationSteppers: {'d': 1, 'h': 1, 'i': 1, 's': 1}, useLang: 'en', lang: { 'en' : { setDateButtonLabel: 'Set Date', setTimeButtonLabel: 'Set Time', setDurationButtonLabel: 'Set Duration', calTodayButtonLabel: 'Jump to Today', titleDateDialogLabel: 'Set Date', titleTimeDialogLabel: 'Set Time', daysOfWeek: ['Sunday', 'Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday'], daysOfWeekShort: ['Su', 'Mo', 'Tu', 'We', 'Th', 'Fr', 'Sa'], monthsOfYear: ['January', 'February', 'March', 'April', 'May', 'June', 'July', 'August', 'September', 'October', 'November', 'December'], monthsOfYearShort: ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'], durationLabel: ['Days', 'Hours', 'Minutes', 'Seconds'], durationDays: ['Day', 'Days'], timeFormat: 24, headerFormat: '%A, %B %-d, %Y', tooltip: 'Open Date Picker', nextMonth: 'Next Month', prevMonth: 'Previous Month', dateFieldOrder: ['m', 'd', 'y'], timeFieldOrder: ['h', 'i', 'a'], slideFieldOrder: ['y', 'm', 'd'], dateFormat: '%Y-%m-%d', useArabicIndic: false, isRTL: false, calStartDay: 0, clearButton: 'Clear' } } }