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When Henry Morgan captured the French privateer ship, "Le Cerf Volant" he rechristened it the "Satisfaction" and used it as his flagship until it was lost near Panama in 1671 during a mission to capture a Spanish fort, the Castillo de San Lorenzo. A wreck some believe is the Satisfaction was found in 2011 by a team of archaeologists funded by the Captain Morgan's Rum company.

I cannot seem to find any resources that say when Henry Morgan captured the ship.

What date did Henry Morgan capture the "Satisfaction"?

Le Cerf Volant, a 14-gun warship, was probably captured in late December 1668 (New Style date) by Edward Collier while commanding the Oxford. Collier seized the French ship at Cow island while it was anchored not far from Morgan's ship.

According to Dudley Pope in Harry Morgan's Way: The Biography Of Sir Henry Morgan 1635-1688 (2013), Sir Thomas Modyford, governor of Jamaica, gave Edward Collier command of the Oxford and ordered him to follow up on a complaint that Le Cerf Volant was a pirate. After this, Collier was to join Henry Morgan, who had been given the rank of admiral in January 1668 with orders "to take action against the Spanish". According to Pope,

Collier guessed that he could carry out both orders at Cow Island
because Morgan was there and the French ship had probably joined him...

As the Oxford sailed into the Cow Island anchorage and fired a salute
to Morgan (who was seeing the frigate for the first time), Collier
sighted Le Cerf Volant anchored nearby….

Following the arrest of the French captain and his crew, Collier

brought into Port Royal the captain and forty-five-man crew of Le Cerf
Volant (fourteen guns) of La Rochelle, clapped in irons and accused of
plundering a Virginia merchantman. Sir James Modyford, the governor’s
brother, had no difficulty in condemning the unfortunate French
master, although he was later reprieved, and his ship was condemned as
a lawful prize.

Source: Jon Latimer, 'Buccaneers of the Caribbean: How Piracy Forged an Empire' (2009)

Renamed Satisfaction, the newly acquired ship and the Oxford sailed back to Cow Island for a rendezvous with Morgan. The Oxford blew up shortly after, on January 12th (New Style), when the powder magazine was ignited by a spark. Morgan and Collier, who were on board at the time, survived but around 200 others perished.

The exact date is hard to pin down but, according to Pirates of the Americas by David F. Marley, Collier left Port Royal (Jamaica) for Cow Island (Haiti) on Dec 20th (this appears to be a New Style date, so Dec 10th old style) and the Oxford blew up on Jan 12th (Jan 2nd old style) after returning, again from Port Royal. This makes a late December (New Style) date most likely for the seizure of Le Cerf Volant.

As near as I can find, the Cour Volant was captured by Edward Collier in December 1668 at the Isle à la Vache, off the harbour of Aux Cayes in Hispaniola. Collier was, at that point commander of the frigate, Oxford, having been given command in early November 1668.

The Oxford was blown up, and Collier took the newly named Satisfaction as his flagship in January 1669. According to the The life of Sir Henry Morgan by E.A. Cruickshank, the explosion that destroyed the Oxford occurred on 2 January 1669. The Cour Volant must therefore have been captured before that.

Details are recorded in the Calendar of state papers, Colonial series. America and West Indies as follows:

Feb 18 [1669] Port Royal, Jamaica: Richard Browne to Williamson. Gave him account about a month since of the unhappy blowing up of the Oxford Frigate and the taking of M. La Vivon, of the Cour Volant, of 18 guns and 10 petarders, which was condemned as a Pirate; she is now called the Satisfaction, and victualled for four months, to go as a Privateer
against the Spaniards in the Bay of Campeachy ...
Indorsed : Rec. 4 May. 1 2)- [Col. Papers, Vol. XXIV., No. 18.]