I do not know if I would label it as a 'counter-crusade', contemporaries certainly would not have articulated it in such a manner, but the Almoravid expansion into Al-Andalus in the second half of the eleventh century could be read as such a reaction to developments in the Iberian Peninsula during the eleventh century.

First, a caveat. The Almoravid expansion was not a reaction to the Crusades exactly --the initial expedition took place in 1086. However, the rhetoric and realities surrounding Christian conquests in the peninsula places them firmly within the same tradition. Historians have argued over to what extent the conquests in Muslim Spain prior to the twelfth century can be labeled as crusades. The wars were sanctioned by the papacy, had an international character in the form of French participation, and were framed as a general Christian offensive against Islam. However, they lacked the focus on reclaiming the Holy Land, indulgences, and the wearing of the cross. The question is an important one, but it is largely semantic. If you will indulge me, I think we can move forward with the understanding that the eleventh century conflicts between the Christians kingdoms of northern Spain and Muslim Al-Andalus were situated by contemporaries within the same framework of a holy war that pitted Christendom against a non-Christian other.

The eleventh century had been a bit of a whirlwind for the Muslim rulers of Al-Andalus. In 1000 the Caliphate of Cordoba was the premier power in the peninsula and was likely the richest polity in all of Western Europe. United under the de facto rule of Muhammad ibn Abi Amir al-Mansur, the armies of the caliph annually raided the Christian kingdoms and counties in the north of the peninsula, including a particularly devastation sack of Santiago de Compostela in 999. However, within thirty years of al-Mansur's death in 1002, the caliphate had collapsed in the wake of a disastrous series of civil wars following an attempt by one of al-Mansur's sons to install himself as caliph. The territory of the caliphate fragmented into a myriad of small kingdoms and polities, initiating the Taifa period of Islamic rule in the peninsula, so named for the muluk al-tawa'if or kings of the regions.

The response of the Christian kingdoms to the sudden collapse of caliphal authority was slow, but Christian aggression increased over the course of the first half of the century. While territorial acquisition was certainly a feature of the wars, for most of the period the Christian kings were content to exact tribute in the form of parias from the Taifa kings. The situation was far from ideal and dissatisfaction was rampant among members of the elite, the ulama and other religious figures, as well as among the populace at large, on whom the financial burden for the parias fell. By the 1080s, the most if not all taifas were paying annual tribute to one of the Christian kings or counts of Northern Spain.

The tipping point, however, came in 1085 with the conquest of the Taifa of Toledo by Alfonso VI, the king of León-Castile. In the midst of a rebellion that challenged the power of his client king al-Qadir, Alfonso laid siege to the city, conquering it and claiming it for his own and installing al-Qadir as king of Valencia as compensation. The fall of Toledo was met with alarm by the Muslim community, the kingdom of León-Castile had essentially increased by a third overnight. The poet Ibn al'Assal in particular, captures the desperation and fear of the moment:

O people of al-Andalus, spur on your mounts; it is nothing but a blunder to stay on here.

A robe (normally) unravels from its edges, but I see the robe of the peninsula unraveled from the center.

We are caught up with an enemy who will not leave us alone. How can we live in a basket together with snakes?

It is within the context of these events that representatives from the taifas of Seville, Badajoz, and Granada crossed the Straits of Gibraltar to seek aid from Ibn Yasin and the Almoravids. Begun in the 1050s as a religious movement focused on a strict adherence to a conservative view of Islam, the Almoravids quickly rose to prominence, achieving undisputed control of Morocco by 1083. in 1086, the first Almoravid expedition crossed into the Iberian peninsula where Ibn Yasin's army defeated Alfonso's forces at Sagrajas near Badajoz. In spite of the victory, the allegiance between the Almoravids and the Taifa kings was fraught with quarrels and disagreements as each jockeyed for position in expectation of what they hoped would be a rest oral of the status quo. Following a particularly frustrating failed siege at Aledo in 1088, Ibn Tashfin returned to North Africa.

When Ibn Tasfhin returned to the peninsula in 1090, he did so as a conqueror of his co-religionists. The Almoravid king quickly subdued the Taifa kings, who were unable to put up much of a resistance, and carted them off to exile in Morocco. The Almoravid conquest was met with general approval among the Andalusis, who saw in the Almoravids hope for a restoration of fortunes. The religious elite in particular were vocal in their support of their devout new rulers, and encouraged the people to voice their support for the conquerors and as a consequence, the transition was largely peaceful.

The Almoravids succeeded in preventing further Christian advances until the collapse of the regime in North Africa in the mid-1140s. Near the end, they came increasingly reliant on Catalan mercenaries, an acute reminder of the complexity of medieval politics that often transcended simple Christian vs. Muslim divides. It's also important to remember that Islam was and is not a monolithic identity, and responses to Christian incursions into Islamic lands were not 'coordinated' in the same way that the papacy attempted to direct the armies of Christendom.

TL;DR Almoravid intervention in Muslim Spain was a response to an invitation to free the taifas from the subjugation of Christian kings, who had themselves capitalized on a series of conquests rooted in a rhetoric of Christian holy war.

That at least, is the closest I can get to providing an example. The Almohads (another North African religious movement/polity) would be the successors to the Almoravids in the Iberian Peninsula, but from my understanding were more focused on affairs in Morocco and not as successful in halting the Christian advance.