I'm a certified child safety seat installer for my agency. I have had MANY vehicles come in to put seats in, but never a vintage car. That being said, as long as your seat belts are in good shape (you do inspect them, right?) they should be fine to secure a child seat into a car.
There is a system called LATCH (Lower Anchor and Tethers) that makes it MUCH easier to install modern seats in modern cars. The upside is that manufacturers have LATCH retrofit kits for some vehicles that allow you to put the lower anchors in. Unfortunately they don't go back to the 70's but you may be able to modify the kit to fit. Understand you're taking all the liability at this point. And I said easier, not safer. Seat belts in good condition are just as safe as a properly installed LATCH system. The LATCH is better only because its far easier to use and harder to make a mistake.
Also from a legality standpoint, to my knowledge you can have a child seat in the front of a NON air bag equipped car. Air bags and child seats have been proven fatal when used together (the air bag is expecting a 150 pound adult, not a 7 pound child encased in hard plastic). But before you do, check local laws or run it by the PD. Realize some cops may not know the law intimately so do some digging online for the actual chapter and section if you can find it.
Personally, I'd be fine with putting my child in the back seat (front only if necessary, or parade) with only good safe factory belts holding the seat in.
