Userscript you can use with Fluid App to add a counter to the dock.

fluidapp.fastmail.js

/*
Fluid App Userscript  
FastMail web interface  
URL pattern: *www.fastmail.com*
*/

// For best results, make sure to turn on desktop notifications
// in fastmail. Otherwise the counter will only update every 90s
// instead of instantly.

(function() {
	function debounce(func, wait, immediate) {
		var timeout;
		return function() {
			var context = this, args = arguments;
			var later = function() {
				timeout = null;
				if (!immediate) func.apply(context, args);
			};
			var callNow = immediate && !timeout;
			clearTimeout(timeout);
			timeout = setTimeout(later, wait);
			if (callNow) func.apply(context, args);
		};
	};

	function getFolderCount(name) {
		var folderEl = document.getElementsByClassName('v-FolderSource--' + name)[0];
		if (!folderEl) return 0;

		var badgeEl = folderEl.getElementsByClassName('v-FolderSource-badge')[0];
		if (!badgeEl) return 0;

		return parseInt(badgeEl.innerText.trim()) || 0;
	}

	function updateBadge() {
		var inboxCount = getFolderCount('inbox');
		console.log("Badge = " + inboxCount);

		if (inboxCount > 0) {
			window.fluid.dockBadge = inboxCount;
		} else {
			window.fluid.dockBadge = "";
		}
	}

	var debounceUpdateBadge = debounce(updateBadge, 1000);

	window.setTimeout(updateBadge, 2000);
	window.setTimeout(updateBadge, 5000);
	window.setTimeout(updateBadge, 10000);
	window.setInterval(updateBadge, 90000);

	var oldNotify = window.Notification;
	window.Notification = function(title, opt) {
		if (window.fluid.dockBadge && window.fluid.dockBadge !== "") {
			window.fluid.dockBadge++;
		} else {
			window.fluid.dockBadge = 1;
		}
		new oldNotify(title, opt);
	}

	document.addEventListener('keydown', debounceUpdateBadge);
})();

Are you still using fluid? Mine stopped showing the badge icon and I can't figure out why. The code properly sets the window.fluid.dockBadge property, but the badge isn't shown.