Google Sheets's native way of doing this requires a lot of keystrokes as described elsewhere, but you can now easily record a macro doing the action, in this case inserting a row (Under Extensions->Macros) and assign it a single key command (and modify the source as needed).
Here is what my modified macro (to insert multiple rows) looks like:
function myFunction1() {
var spreadsheet = SpreadsheetApp.getActive();
var numRows = spreadsheet.getActiveRange().getNumRows();
spreadsheet.getActiveSheet().insertRowsAfter(spreadsheet.getActiveRange().getLastRow(), numRows);
spreadsheet.getActiveRange().offset(numRows, 0, numRows, spreadsheet.getActiveRange().getNumColumns()).activate();
};
Since this is also likely relevant to people finding this, here is the (unmodified) macro to delete rows:
function myFunction() {
var spreadsheet = SpreadsheetApp.getActive();
spreadsheet.getActiveSheet().deleteRows(spreadsheet.getActiveRange().getRow(), spreadsheet.getActiveRange().getNumRows());
};