neons like to be in a school of at least 5-6, which pretty much fills the 6 gallon tank imo. may want to stick with smaller fish (i.e. guppies) although I guess since they breed so easily this might be an issue too
I wouldn't put a school of neons in there because of their need for jetting.... you can probably go for a betta or endlers could work but you may have breeding issues eventually because they are livebeares.