To make a purple drink, you need blue and red. The blue will inevitably come from blue curacao, and the probably from either grenadine or cranberry juice.
A shot of blue curacao in about 5 oz cranberry juice is sometimes called a blue sapphire, and will have a reddish-purple hue.
Blue curacao in some champagne or sparkling white, with a splash of grenadine, would make a nice purple spritzer of sorts.
Another option, though a bit stronger drink, would be to make a cosmopolitan martini, but use blue curacao in place of triple sec. Taste will be about the same, but should get the purple color you're after. 1.5 oz vodka, 0.5oz blue curacao, juice from half a lime, splash of cranberry juice, add with ice in a shaker, strain into a martini glass. Stronger drink, but very classy.
You may notice I didn't mention sloe gin as a red option, because I'm not sure how well the flavors will play. I suppose it would be possible to do a variation on the Sloe Gin Fizz, using blue curacao in place of lemon juice (still a citrus flavor, at least), though the lower acidity and higher sweetness may not work as well... maybe I'll experiment this evening and let you know how it goes. That said, it's not such a classy drink to begin with, and is a bit more intensive from a preparation standpoint.
Hopefully, this gives you some ideas at least.