First of all, I assume you mean overall career greatness and not only how good a player was at their very best. Kieran likes to tout Lew Hoad as better than Laver and Rosewall, at least at his best, but clearly the record doesn't bear that out. Hoad goes down in history as a very talented player who could have been one of the greats, but one who didn't have the career to match his talent.
Anyhow, you asked for it so I'm going to go for it. I've done some extensive research on this question and the results are inconclusive, at least if we want to talk about all of tennis history. But if we look at the entirety of tennis history, in my mind there are eight players who stand out above the rest - what I'd call the "Herd of GOATs." In chronological order:
Bill Tilden, Pancho Gonzales, Ken Rosewall, Rod Laver, Bjorn Borg, Pete Sampras, Roger Federer, Rafael Nadal.
Just outside of those eight you have a few players that don't quite make the cut: Don Budge, Jimmy Connors, John McEnroe, Ivan Lendl, and Novak Djokovic (so far; he has a chance to expand the "herd" to nine). Then there's a third group of a dozen or so players which includes players like Renshaw, Larned, Perry, Riggs, Cochet, Kramer, Newcombe, Wilander, Edberg, Becker, Agassi, and many others.
Anyhow, of those eight it is really hard to narrow them down. But if we're going to go through a process of elimination, I'd cut Borg first - mainly because he retired in mid-career. If he had not only played another 5+ years AND rediscovered his passion, he probably would have won several more Slams and be more strongly in the running. But we have to look at what he did, which was remarkable, but below the other seven. Plus the fact that he never won the US Open mars his record.
So now we have seven. What to do next? It is hard to cut any of them. Tilden was the greatest the game had seen up to that point, and the overall most dominant player of two decades--the 20s and 30s--and played all the way into the mid-40s. He supposedly has a historical best career match record of 93.6%, which is just absurd. There were some other players who were as great as him for periods of time in the 30s and 40s, but none for as long as Tilden.
Pancho Gonzales is criminally underrated because he played most of his career as a pro and was banned from the amateur Slams. But he won 17 majors in all and was the best player of the 50s.
Laver is often considered the GOAT for his not one but TWO calendar Slams, and was clearly the greatest player of the 60s and is probably as good a candidate as any. Rosewall was to Laver what Agassi was the Sampras - not as good, but with greater longevity. Rosewall won Slams over a twenty year period of time, from 1953 to 1972, and has more majors than anyone with 23 in all. But he wasn't quite as good as Laver, so that will always work against him.
Borg was the greatest player in the world for a few short years, but never won the second most prestigious tournament in tennis history and quit while still quite young. I already cut him out.
Then we have Pistol Pete, who like Borg had a white whale he was never able to catch: the French Open. We can forgive him because of the tremendous court differences, but his main (and lesser) rival, Andre Agassi, was able to win all four. Pete also retired relatively young for a GOAT candidate.
Finally we have Fedal, who if we want to take the view that the game gets better and better could be considered the greatest players of all time (so far). Roger doesn't really have any negative marks on his record, despite the ghost of the supposed weak era and Rafa's dominance over him. But in terms of career accomplishments, his record is easily the greatest of the Open Era.
A couple years ago it looked like Rafa could take up the mantle. He could still win a couple more Slams, but the big mark on his GOAT candidacy is the lop-sidedness of his Slam record. His non-clay record is great, but not GOAT-great. In order to be considered the sole GOAT I think he needs at least two more non-clay Slams, and maybe a WTF (consider that over the last 40 years, of all 4+ Slam winners only Rafa, Wilander and Courier haven't won the ATP Finals...Vilas, Connors, Borg, Lendl, McEnroe, Edberg, Becker, Agassi, Sampras, Federer, and Djokovic have all won it).
So where does that leave us? Well, there are two ways to do this. One is to talk about best of their era, or of different eras. If we split between pre-Open and Open it makes things a bit easier. I'd say:
Pre-Open Era
1. Laver
2. Rosewall
3. Gonzales
4. Tilden
5. Budge
6. Perry
7. Renshaw
8. Vines
9. Larned
10. Wilding or Cochet
Open Era
1. Federer
2. Nadal
3. Sampras
4. Borg
5. Connors
6. Lendl
7. Djokovic
8. McEnroe
9. Agassi
10. Edberg
(With Newcombe, Wilander and Becker just behind)
If push came to shove, I'd probably rank the fifteen GOATs in this order:
1. Laver
2. Federer
3. Rosewall
4. Gonzales
5. Tilden
6. Nadal
7. Sampras
8. Borg
9. Connors
10. Lendl
11. Djokovic
12. Budge
13. McEnroe
14. Agassi
15. Perry
I have some time this summer and once I get through my current article lineup, I'll do a more exhaustive study and write a blog about it.