I guess by “bastille” you mean a recipe that is mostly olive oil, with small additions of a few other oils? There is no agreed-upon definition of this type of soap, so you're technically free to replace anything with anything else and call it that way.
BUT you are aiming at some particular function: avoiding coconut oil. CO serves a particular purpose in soap, and it depends on a few things what it is best replaced with.
First, your niece. That's a bummer
. Wrt soap, it would help a lot to know if she has a allergy specifically against
Cocos nucifera, or rather an intolerance to soaps with lauric acid. In the former case (aka lauric soaps are okay, but CO is a no-go), the obvious replacement for CO is palm
kernel oil/flakes (or, if you can get/want to afford it: babaçu or murumuru). Thing is, these are from palm tree seeds too, and someone with a CO allergy might or might not be sensitive to these as well.
The only other common soapmaking oil that offers lauric acid (= bubbles and cleansing factor), is laurel berry oil, that would make an Aleppo-type soap.
Palm oil (from the
pulp of the oil-palm fruit) is an entirely different oil than coconut oil. Adding it to a mostly-olive soap won't help you at all with a more lively lather, nor will it boost the cleansing action of the soap. It does help with hardness and increase the life span of the bar, though. Of course you can add palm oil to olive soap, but don't expect it to cheer up its otherwise quite dull and hesitant castile character, quite as quickly as CO would do.
If you were adding coconut oil for the lather, don't forget the other tricks to increase bubbliness of soap! Some % of castor oil, add sugar/sorbitol to the lye, use aloe vera juice instead of water. And at usage time: use a soapcloth (bar soap) or a foamer bottle (liquid soap).