Rome did have Sparta as an ally! For a bit at least - they also fought Sparta, so I guess you could describe their relationship as "It's complicated". The answer below is a slight adaptation of this answer I gave some time ago (under my previous account).

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By the time Rome got involved in Greece Sparta was in a state of being past-their-prime-but-not-yet-irrelevant. Sparta remained a proud and independent city-state, but it wasn't really a major player any more. Sparta was the only Greek city not siding with (or forced to side with) Alexander the Great in his campaign against the Persians in the late 4th century. It was just capable enough to withstand Macedonian pressure, but it wasn't nearly powerful enough to be a threat to Alexander or his Greek allies (indeed Sparta had lost another major battle against Greek forces only a few years earlier).

It is a century later that we see Roman involvement in Greece starting. During the First Macedonian War (late 3rd century BC) Rome sought the help of the Aetolian League, granting the rights of amicitia (friendship) to the Aetolian League and any city state helping Rome in the war against Philip V of Macedon (Rome was at the same time fighting the Second Punic War, so it had limited resources available for the war in against Philip V). Sparta sided with Rome in this war, and so became an amicus of Rome.

Being an amicus was somewhat short of being an ally; it was certainly not a defensive pact and dit not guarantee any protection from Rome. So it happened that Sparta in 201 attacked Messene, another amicus of Rome, and in 198 - during the Second Macedonian War - Sparta made peace with Macedon even though Rome remained at war with them. Pragmatic as always, the Roman Senate revived the amicitia with Sparta the next year, under condition that Sparta would assist in the conflict.

At the end of the conflict, Rome threw Sparta's actions back in their face. Livy reports that the Romans said this to Nabis, the Spartan ruler:

Though you were our ally you seized by force a city in alliance with us, namely Messene, which had been admitted to our friendship and enjoyed precisely the same privileges as Lacedaemon [Sparta - ed.]. And further, you not only concluded an alliance with Philip, our enemy, but you actually established a relationship with him through Philocles, one of his viceroys. In open hostility to us, you infested the sea round Malea with your piratical barques, and have seized and put to death almost more Roman citizens than Philip, so that our transports, which were supplying our armies, found coasting along the Macedonian shores safer than rounding the Cape of Malea. Forbear henceforth, if you please, to talk about your loyal observance of treaties; drop the language of a citizen and speak as a tyrant and an enemy. (Livy 34.32)

As Rome had given many Greek cities their liberty by defeating Philip V of Macedon, so too would they give liberty to the city of Argos, which was under Spartan occupation. Under this pretext Sparta was attacked and defeated by Roman and Greek forces, ending whatever remained of the Spartan hegemony in Greece. Sparta was forced to join the Achaean League.

For the next fifty years or so Rome remained involved in Greece while proclaiming that the Greek cities were free. During the Third Macedonian War (171 – 168 BC) Rome took prominent members of Greek communities as hostages to Rome, to ensure the continued loyalty of the "free" Greek cities. Eventually, after the final defeat of Macedon in 148 and the incorporation of Macedon in the Roman empire, it came to war between Rome and the Achaean League. The catalyst, interestingly, was Sparta.

Since Sparta was forced into the league, it continuously tried to leave the league. At least three times the Spartans or Spartan exiles petitioned Rome with challenges tot he jurisdiction of the Achaean League, each petition being counter petitioned by representatives of the league. As Erich Gruen put it:

Senatorial reaction was cast in the traditional mold: evasive and noncomittal answers which each party read in accord to its own wishes and employed to justify steps already determined upon. (p. 520)

Finally Sparta seceded from the league, and the Achaean League responded with force. They figured this was an intra-Greek conflict; the Greeks were nominally free and Rome had so far proven to be mostly indifferent to what happened. Rome responded swiftly and decisively though. Roman forces moved from Macedonia and Italy into Greece and crushed the Achaean League. From then on Greek cities were no longer allowed to form confederations. Some cities - those which had resisted - were put under control of the Roman governer in Macedonia; others, including Sparta, remained "free". It would take another century before this charade was dropped and Greece was made into an official province of Rome. By then the Greek city-states had lost most of their relevance, except perhaps to serve as cultural guides (the Romans of that time loved Greek culture).

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Sources

As said above, I used this answer and adapted it slightly.

• Erich Gruen, The Hellenistic World and the Coming of Rome (Berkeley 1984)

• W.V. Harris, War and Imperialism in Republican Rome 327-70 BC (Oxford 1979)

• A.M. Eckstein, Senate and General: Individual Decision-making and Roman Foreign Relations 264-194 BC (Berkeley 1987)