If your house is that crowded I'd suggest a hamster since its just as fun and smaller cage. Try to rescue the little creature but if you can't find an animal orphanage around your area, Go to your local petstore. 10-15$ for hamster, 20-25$ for cage, + food, bedding ect.
Tell them that you want some responsibility, that you'll take full 100% care of the animal, you won't neglect the little guy and that you'll do extra work around the house. If your cats are jumpers try to put the cage in a room where they usually don't jump, cant jump or aren't allowed. Don't try and let your hamster play with the cat.
If all else fails, take them to the pet store, let them hold the little guy and watch them fall in love!
you need to decide which rodent fits your lifestyle best.
Dont need alot of handling--but enough to feel loved and cared for
Sleep during the day
Dont take up much room
Sometimes hard to handle
Love being handled
Need lots of attention
Buy in pairs or groups
Make cute squeeking noises to say when their happy
Take up some room (depending if their inside or outside)
Hope this helps! :)
Let me know what you got
tell her you will adopt one which is cheaper and tell her adopting a guinea pig would be saving its life because there are actually alot of guineas at the shelter and guinea pigs are more likely to be put down than to be adopted. i personally think guinea pigs are the best rodents just cause there nice and dont bite. tell her to think about it and give her some time to think about it. if she says no then theres not much more you can do about it besides asking for a diferent pet
If your house is crowded and you have cats, I would suggest a hamster would be a better option. The hamster is easier to take care of, wouldn't be in risk of having the cat jump in the cage, and don't take up a lot of space. Anyway, to convince them to get a pet, first, do a lot of research about the pet you decide on. Make a powerpoint or report on it and present it to them, with a well thought-out plan of how to keep it away from the cats.
Then, do a lot of things around the house. Take care of the cats without being asked, clean your room or the house without being asked, be careful with money, etc. Tell them it'll make you feel good having a pet to take care of that's yours and yours alone. Explain it would teach you responsibilty and make you feel good. Good luck! Hope I helped.