One way to achieve this is by using the angular date $filter to format a date as desired, as it does not provide an easier method for manipulation.
For adjusting the day:
var myDate = new Date();
var previousDay = new Date(myDate);
previousDay.setDate(myDate.getDate()-1);
var nextDay = new Date(myDate);
nextDay.setDate(myDate.getDate()+1);
Manipulating the month:
var previousMonth = new Date(myDate);
previousMonth.setMonth(myDate.getMonth()-1);
var nextMonth = new Date(myDate);
nextMonth.setMonth(myDate.getMonth()+1);
Changing the year:
var previousYear = new Date(myDate);
previousYear.setYear(myDate.getFullYear()-1);
var nextYear = new Date(myDate);
nextYear.setYear(myDate.getFullYear()+1);
$scope.month = $filter('date')(myDate, 'MMMM');
$scope.day = $filter('date')(myDate, 'dd');
$scope.year = $filter('date')(myDate,'yyyy');
$scope.nextDay = $filter('date')(nexyDay, 'dd');
$scope.prevDay = $filter('date')(previousDay, 'dd');
$scope.nextMonth = $filter('date')(nextMonth, 'MMMM')
$scope.prevMonth = $filter('date')(previousMonth, 'MMMM')
$scope.nextYear = $filter('date')(nextYear,'yyyy');
$scope.prevYear = $filter('date')(previousYear,'yyyy');
If you anticipate frequent use of this code, consider creating a service to streamline the process.