What year did Cessna put the Lycoming 320 in the 172?

1968 was the year. All of those engines were earmarked for the Cessna 177/Cardinal until they realized it was underpowered on 150HP You are looking for a 172 I or later (except the P172, the 172Q, the 172RG, the 172XP, or any of the restart Cessnas like the 172R and SP).

Not only is the 320 the preferred engine, but there are versions of the 320 which are preferred as well. You want the O-320-E2D which is from the I to the M models. The N added 10 HP with the H2AD, but they are very prone to eating camshafts even after tons of mods and additives and have the dual magnetos where both are driven by one drive. The Ps are a bit better with the O-320-D2J, but I'd rather have the E2D and ten less horsepower, as even 30 more with an O-360 aren't noticeable.

The best model is probably the M. They still have 40 degrees of flap but also have the leading edge cuff which makes them handle very well at low speeds. Aside from the engine, the better ones are probably the straight tails. They are lighter, have better visibility, are faster, have a smoother engine, and have just about nothing that can go wrong with them (venturies instead of vacuum pumps, mechanical fuel gauges, mechanical flaps, no starter solenoid). Find one with a recent engine overhaul for half the price of a newer 172 and enjoy.

Hundreds of older 172s have been converted to Lycomings. It's a very common conversion (and FAA approved) so don't pick one based solely on the model year.

1968 C-172L