I do have an hCG approved makeup list.
as well as a quick article on whether or not being oil-free with our personal care products really matters or not.
As far as just a couple of quick suggestions though:
Clinique Stay-Matte Oil-free (has good reviews on Amazon too)
Laura Mercier Silk Creme Oil-free (a pricier brand but a fav of makeup artists – maybe a new go-to for regular life??)
NARS All Day Luminous Weightless Oil-free