Passover isn't usually associated with classic cocktails; it's more commonly associated with the overly sweet Manischewitz wine. But now that the kosher wine market is exploding, it's only natural that kosher cocktails followed suit.
Of course, don't think that you can simply start handing out shots of whiskey at your Passover seder — first off, that's just inappropriate, and secondly, it's not kosher. All spirits must have a Kosher for Passover certification, different from a kosher certification. So while you can enjoy many kosher spirits during other parts of the year, most are forbidden during Passover.
So what does that leave you to drink at Passover? Southern Wine and Spirits of California shares a list of kosher-for-Passover spirits that willl make your drinks that much more fun: 209 Kosher for Passover Gin and Vodka, Sabra Liqueur (a big favorite for Hanukkah cocktails, as well), and Casa Vieja Añejo Tequila, among others. While it may take some dedicated trips to the liquor store, there are lots of kosher-for-Passover spirits options.
Obviously, the next step is the cocktails. While it's more traditional to be drinking wine during the seder, you can add some cocktails to the mix thanks to the Sipping Seder handbook. Yes, really: cocktail enthusiasts Rob Corwin and Danny Jacobs created a seder plate with dedicated, kosher-for-Passover cocktails that will make your heart sing. The Maror cocktail uses the traditional bitter herbs consumed at the seder, horseradish; and the Karpas cocktail uses one of the herbs to signify the coming of spring, parsley. Corwin and Jacobs have literally planned out your cocktail menu — so get to it.