Code snippets helps to enable the SharePoint Designer Access to the Site Collection

enableSiteDesignerAccess.js

//Author: Shantha Kumar T
//Property used: SP.Site.allowDesigner (sp.js)
//Supports SharePoint 2010 + and SharePoint Online

function enableSiteDesignerAccess() {
    var clientContext = new SP.ClientContext();
    oSite = clientContext.get_site();

    //The below line helps to enable the designer access
    oSite.set_allowDesigner(true);

    clientContext.load(oSite);
    clientContext.executeQueryAsync(
        Function.createDelegate(this, function() {
            var siteInfo = '';
            if (oSite.get_allowDesigner())
                siteInfo = 'Designer Access: Allowed';
            else
                siteInfo = 'Designer Access: Not Allowed';
            alert(siteInfo.toString());
        }),
        Function.createDelegate(this, function(sender, args) {
            alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());
        }));
}

function injectMethod() {
    enableSiteDesignerAccess();
}
ExecuteOrDelayUntilScriptLoaded(injectMethod, "sp.js");