There are routers that can't do that? O.O from the cheapest Chinese ISP piece of crap (*cough* Zyxel *cough*) to my AirPort Extreme, I've never seen one that didn't have some kind of static option.
Yes, there are, depending on make/model and how much you are willing to spend.
Way back in 2008 I picked up a D-Link WBR-1310. Cost me less than $100 but I soon found out why.
After figuring out how to arrange my network so that it became a wireless bridge (WAP) to the wired network I soon discovered that it was cheap for three reasons.
One, there was no allowance to set static IPs and no port forwarding. I had to rely on my wired router for that. Two, once my wife started getting and using wireless devices we then found out that any time a new device connected to the router it bumped off a previous device!
And three, over time the firmware stopped recognizing the username and password to access the web interface. If I tried to access it and there was no username/password box, I had to reboot the router.
I finally replaced the damn thing with a Linksys WR54GL but the precedent of using my wired router for assigning static IPs was set.
That crap Dlink router is now in the garage. If I ever get around to setting it up again it'll be put to use simply as a repeater or network extender.
P.S. My 2004 D-Link wired router is still going strong. It's been on for 11 years now!