Every game on this site started as somebody's family game. If yours isn't here, describe it and we'll build it. There's no charge and no account — we just need enough detail to get the rules right.
The thing that stalls a game is almost never the code — it's the rules. Card games in particular vary from family to family, and an approximation is worse than nothing, because a game with the wrong rules just causes the arguments it was meant to end.
Mahjong for four players, and better tools for people who play with the same group regularly — planning a party's games in advance, and carrying a scoreboard from one night to the next. If either would be useful to you, say so in the form; it moves things up the list.
Every game here is free, runs in a browser, and needs no app or sign-up. One person creates a game, shares the link, everyone plays on their own phone.