Kiddush on Shabbat morning should preferably be recited over either wine or grape juice. If one cannot drink wine or grape juice, or if one does not have access to wine or grape juice, then Halacha allow reciting Kiddush over "Hamar Medina," an intoxicating beverage that is commonly drunk in his area of residence. In contemporary times, the most common example of "Hamar Medina" is beer. Therefore, a person who, for whatever reason, cannot recite Kiddush over wine or grape juice should use beer for Kiddush. He should recite the Beracha of "She'hakol Niheya Bi'dvaro" and drink a Revi'it – approximately 3 ounces – of beer.
If a person cannot recite Kiddush over wine, grape juice or beer, is there any other beverage over which he may recite Kiddush?
Maran (Rabbi Yosef Karo, author of the Shulhan Aruch), in his work Bet Yosef (Siman 289), rules that in such a situation one may recite Kiddush over any beverage other than water. According to this view, one who does not have access to wine, grape juice or beer may recite Kiddush over any fruit juice or even cola. In the Shulhan Aruch, however, Maran retracted this ruling and required that Kiddush be recited over only "Hamar Medina" where wine and grape juice are not available.
As for the final Halacha, Hacham Ovadia Yosef, in his work Yabia Omer, Helek 3, O"H, Siman 19, rules that one who cannot drink wine or grape juice should certainly recite Kiddush over beer, in accordance with the ruling of the Shulhan Aruch. Nevertheless, if a person does not have access to beer, either, then he should recite Kiddush over a beverage other than water and then conduct his Shabbat meal over bread. Since the Kiddush recitation on Shabbat morning consists of only the Beracha over the beverage, using a different beverage does not entail the risk of a Beracha Le'vatala (a "wasted" Beracha). The only potential Halachic dilemma relates to the prohibition against eating and drinking before Kiddush: if Halacha does not allow one to fulfill the Kiddush obligation with other beverages, then one who does so will have drunk and eaten without reciting Kiddush. As Hacham Ovadia notes, however, some Rishonim (Medieval Halachic authorities) permit eating and drinking before Kiddush on Shabbat morning, and thus in a situation where wine, grape juice and beer are not available, one may rely on these authorities and recite Kiddush on any beverage other than water.
Summary: On Shabbat morning one should recite Kiddush specifically over wine or grape juice. If one cannot drink wine or grape juice, or does not have access to wine or grape juice, he should recite Kiddush over beer. If he cannot drink beer or does not have access to beer, then he should recite Kiddush over any beverage other than water.
