How old is the child? Is she old/big enough for a booster seat or does she need one that attaches with the LATCH or seatbelt? How many children do you keep at a time?
I would ask the parent to buy a carseat that you can keep all the time. If they won't, I would buy one yourself.
I have 2 kids (age 4 and 6). Both of my kids rode in Britax car seats that use the LATCH system (my son in the Husky and my daughter in the Regent) until my son got too big to use the LATCH. He fit the car seat weight wise but I did not feel it was secure with the seatbelt holding it in. I nmoved my son to the Britax Parkway booster seat. My daughter is still in her regent. I use my son's old Husky (which is safe up to 40 pounds using the LATCH) for transporting my daughter's friends. I bought a 2nd Parkway booster for transporting my son's friends. Now, I am always equipped to transport 4 kids at any time without having to worry about moving carseats.
The Britax car seats are the best. However, they are pricey and HEAVY and hard to move from car to car. I won't move my daughter's. I would rather have her friend ride with us than to move her carseat. My husband also has a Regent and a Husky in his car (his car is safe up to 60 pounds for the Husky using the LATCH so my son can still ride in it)
Car seats can be difficult to install unless they are the booster seat that is held in by the chil's weight and seat betl. In an emergency, I would be too stressed out anyway and would not want the extra worry of having to install a car seat properly. Could you leave the car seats in your car all the time? When I was in college, i babysat for a family over the summer. The 2 older kids were old enough not to need a car seat but I kept the 2 year old's seat in my car all summer. Hope this helps.
I just read some of the other comments and your response. Please do not buy a used car seats! Car seats expire after 5 years. Also, you don't know if it may have been damaged in an accident. Just because it looks ok doesn't mean it is.
The 9 month old will need to ride rear facing until she is 1 year old AND 20 pounds. You can buy a covertable car seat that can be rear facing for now and forward facing after 1 year. There are some great websites online. Look for sales. When they introduce new patterns they usually sell the old patterns at a discount. Try www.albeebaby.com or www.babyuniverse.com.
If you had to take 1 child to the hospital, what would you do with the other children? Would you take all the kids with you or is there someone else that helps you that could stay home with the other kids?