I use a Centech pinpoint probe (about $20) & I probe for the coin with a screwdriver, then just move the screwdriver a fraction of an inch & pry up. Usually pretty hard to see where I've been
Hope the state park won't give you any trouble. Whether it's OK seems to depend on who you talk to. Another person that works there might still ask you to leave, but if you're neat & tell them you got permission, they probably wouldn't do anything worse than ask you to leave.
I remember back in the late '70s WI state park ranger told someone they could detect, but to show their finds in case anything rare & historical was found. The ranger demanded that they hand over even the memorial cents. Good luck & HH, George (MN) (30 mi W of Prescott).