It's possible a generous DM would allow the 8th-level druid spell speak with anything [div] (Masters of the Wild 94) to facilitate communication with magical beasts possessing Intelligence scores of 1 or 2, the description saying the spell "enabl[es] you to communicate with any living creature, including unintelligent ones," but the spell's effect also says it merely duplicates the effects of the spells speak with animals, speak with plants, and tongues, and that list of spells—as you already know—doesn't technically include the ability to communicate with magical beasts possessing Intelligence scores of 1 or 2.
Likewise, a generous DM may allow the spell tongues—not normally a 3.5 druid spell—to be cast on the magical beast, allowing the magical beast to talk for the duration! Despite the obvious problems of getting close enough to touch successfully the magical beast and that the magical beast's allowed a saving throw against a spell it (probably?) can't identify, the game doesn't appear to have anticipated this sort-of hostile use of the spell tongues against a creature lacking language, and, when used this way, the DM may reasonably rule that an affected creature still can't talk.
Thus, short of the extraordinary ability tongue of the sun and the moon that's possessed most often by a high-level monk, a level 6 character with a Constitution score of 13 can take the feats Shape Soulmeld (beast tamer's circlet (Magic of Incarnum 60)) (MoI 40) and Open Least Chakra (crown) (MoI 39-40) and bind the circlet to the crown chakra.
Thereafter, during a round in which the wearer has essentia invested in the soulmeld (likely requiring a third feat), the wearer can use an effect like the spell speak with animals (PH 281) except that the wearer can also speak to magical beasts that possess Intelligence scores of 1 or 2.