There are canonically (as far as my research leads me to believe) NO Constitution-class starships in service in the TNG era.
All of the surviving original Constitution-class ships were refitted around 2270 in order to prolong their lives until the 2290s as the following quote indicates:
In the late 2260s to early 2270s, the Constitution-class starships
underwent their final major refit program. The actual refitting took
eighteen months of work and essentially a new vessel was built onto
the bones of the old, replacing virtually every major system. Thus,
the Constitution-class continued in service for a further twenty
Major changes were made to the interior of the Constitution-class
starships; many new systems were added and existing ones upgraded.
Summarizing, only the internal structure of the saucer and very little
of the engineering hull and neck may have survived the 2270s refit.
(Star Trek: The Motion Picture)
Some refit configurations had the warp nacelles rotated 90 degrees and
included additional hatches along both sides of the saucer. (TNG:
Other TOS-movie era starship types that have survived until TNG were all designed specifically in the 2260s and 70s using the Constitution refit technology which is obviously more robust and future-proof than the original Constitution designs. Miranda-class, Obert-class and Excelsior-class have all thrived through to the TNG era because they could cope with the upgrades and modifications needed through the 70 or so years of service and proved to be versatile designs. It could be postulated that the first dedicated, long-service starships, the Constitution-class, were the prototypes for human deep-space exploration and were not designed to be futureproof. 2260s and 70s designs may have been designed specifically for longevity and for ease of upgrade.
That all said, there is ONE example of a Constitution-class ship that was in service up to the battle of Wolf 359, because the wreckage of one is visible in the scene where the Enterprise D arrives at the battle site:
The saucer of one is apparently visible too, just before the ad break following the same scene:
The Ex Astris Scientia website identifies the model used for this scene as the destroyed Enterprise model from Star Trek III, and this has been inferred from information provided by the production staff but never confirmed as canon.
The screenshots are the only evidence of the existence of a Constitution class ship being at Wolf 359 and the only canon evidence of a Constitution-class in the TNG era.
So the final answer I would give is that there was a total of one Constitution class ship in service until 2366, where it was destroyed at Wolf 359. I myself prefer to take the opinion that there were none, and that the existence of Constitution parts in the Wolf 359 debris was simply a production decision that has never been made canon - the Ex Astris Scientia page I linked to above contains a lot of text that indicates the production staff wanted to deny the existence of the Constitution class stuff in the wreckage.