Objective-C, 129
main(){int i=10;while(i-->0)printf("%c",[(i%2==0)?@"aeiouy":@"bcdfghjklmnpqrstvwxz"characterAtIndex:arc4random()%(6+(i%2)*14)]);}
With the help of Daniero
(I love to use the tends to operator (-->)
Objective-C, 129
main(){int i=10;while(i-->0)printf("%c",[(i%2==0)?@"aeiouy":@"bcdfghjklmnpqrstvwxz"characterAtIndex:arc4random()%(6+(i%2)*14)]);}
With the help of Daniero
(I love to use the tends to operator (-->)