Short answer - NO.
Single tailed varieties gets to be 12+", and really need a pond.
Fancies get to be 4-6" and will still be too big for a 4g. Even keeping babies in such a small tank requires a lot of work to prevent disasters, and definitely not for newbies. Esp. when kids are involved, you are setting them up for a lot of heartaches. If you want golds to live more than a month or 2 (the typical miserible lives of the ones kept in bowls & small setups), you need at least a 20 gal.
For a 4 gal, I would suggest a betta or may be a dwarf gourami. If you have an unheated tank, a couple or 3 white cloud minnows.