I think a lot of it depends on age of your characters and their location. A lot of southern kids call their dad's 'daddy' their whole lives and kids there never use first names alone. My 21 year old brothers still do with their dad. For gay friends I've had, biology has nothing to do with it, if they are both around from birth they are both parents so some depends on when the non-bio dad comes into the picture. If they're both around from day 1 they need more intimate names, Daddy/Dad, Pop/Papa. I grew up in the Pac NW for the most part so a kid using the name of an adult close to them doesn't seem weird to me, which is another way location comes into play. In a story I wrote the 3 year old son of my main character calls his father, Daddy and the 2nd who has been around a year, 'Petey'. A combo of 'Daddy P' or something like that would suffice.