No can do thats what makes it so challenging!!!

Nope. But you can hit the Carry Passengers target when lit and it will
hold the passengers you have picked up over to the next ball.

It does! Oh wait, this is a question, huh?

Carry Passengers target
Immediately to the right of the JOYRIDE hole. Lit for about 10 seconds by making all three LOLA or the PINBOT drop banks (whether lit or not). Available from both flippers, but much easier from a left backhand.

Taken from: http://pinball.org/rules/taxi.html

You can make Carry Passengers stay lit longer in the adjustments menu via service switches. It's a hard target to hit intentionally, I'm afraid.

You could also install Extra Easy (or easy, as I don't remember if both are available on Taxi). It should make the game less brutal.

You could put rubber bands across the outlanes when your kids play it, then it would only drain between the flippers.

Also make sure to clean and adjust the switch. Get the gap between the switch blades nice and close, so that a light shot or a rebound off something else will trigger it. A credit dot appeared on mine because the switch hadn't been hit in so long. It would work in switch test, but anything less then a direct solid hit wouldn't trigger it. I cleaned it and closed the gap and it became much easier to collect. I'd recommend this for any Taxi, not just one that kids play.

One of the settings also keeps all the passengers available for pickup all the time. That might be the setting schonb25 referred to.