Some sources mention a genitive singular alius, but I've also seen aliae. And I don't recall seeing a dative singular ali, but neither do I remember alio. I think several forms exist, including even suppletive forms like alterius. What would be standard for Cicero?
Lateinische Grammatik (Leumann, Hofman and Szantyr 1977) argues that
"Im Genetiv ist -īus die Standardform der Endung, sie gilt für Plautus und für die klassische Prosa verbindlich. In metrischen Texten bestehen zwei Nebenformen" (Para 376B2a, p. 479) [emphasis mine - Alex B.]
They also add that "Einigermassen häufig sind nur gen. -i und dat. fem. -ae" (p. 480). They admit that the evidence is shaky, cf. "manche Zeugnisse sind unsicher."
Varro, De Lingua Latina 9.62 alii generis
Plautus, Capt. 306: qui imperare insueram, nunc alterius imperio obsequor. [GEN]
Plautus, Bacch. 462: erum ingenium plus triginta annis maiust quam alteri. [DAT]
Here's a screenshot of the OLD entry.
Note that the OLD lexicographers mention that alterius is sometimes used instead of alius.GEN.SG For more elucidating examples/information, we need to look it up in TLL.
Bennett gives gen. alterius, dat. aliī. Allen and Greenough list alius among the adjectives that "have the Genitive Singular in -īus and the Dative in -ī in all genders", implying alīus, aliī, but add in notes that "Instead of alīus, alterīus is commonly used" and that "The regular genitive and dative forms (as in bonus) are sometimes found in some of these words: as, genitive and dative feminine, aliae; dative masculine, aliō". These possibilities presumably reflect Ciceronian and general Classical usage; it's hard to verify this with a search, though, because all the variants happen to be ambiguous with other case forms.
Gildersleeve and Lodge, §76.r1: The Gen. alīus is very rare, and as a possessive its place is usually taken by alienus.
§76.r2: …usually make the Dat. Sing. in -ī … Alī is found in early Latin for aliī.