Lauric oils, that is, coconut and palm
kernel oil (and a few more obscure ones) usually contain about half by weight of lauric acid, and 15…20% myristic acid. The only oils with considerably higher myristic acid content are ucuuba and nutmeg (both of which are highly “obscure” in the soapmaking context). Go-to resources for palmitic acid are palm oil, palm stearin, or japan wax.
Either of the three acids are also easily available as chemically pure ingredients (though this will alter the behaviour when adding KOH and make things more hectic). If you, for whatever reason, want to avoid unsaturated FAs, this is the easiest and most precise method in any case.
If you're fine with some oleic acid, I'd recommend you fire up the
soap calculator of your choice, add palm stearin and coconut oil, and play around with the percentages until you hit your desired FA profile.
You can easily look up the fatty acid profiles of all common oils here:
http://soapee.com/oilsSelect “Fatty acids – Common” and sort by whatever acid you're aiming at.