Instead of doing this in fits and starts like seasons 1 & 6, I did manage to go through my season 2 DVDs all at once. So these are all I found, I don't expect to add any more to this one.
(This will be updated as some of these vehicles are better identified.)
2.2
Studebaker Lark, one star
1958 Mercury Park Lane, one star
2.3
1961 Ford Thunderbird, three stars
2.5
1955 Ford Fairlane Sunliner, three stars
2.9
1954 Chevrolet pickup, two stars
Chevrolet Suburban 3116, two stars
2.11
1961 Ford Country Sedan, two stars
2.13
1956 Ford F-100, two stars
1959 Chevrolet Biscayne, two stars
2.15
Chevrolet pickup, unknown year, two stars
2.16
1961 Mercury Comet station wagon, two stars
Buick, unknown year, one star
2.17
1940 (?) Ford pickup, two stars
2.18
1962 Ford Galaxie 500 (foreground), two stars
1961 Ford Econoline pickup, one star
1960? Ford F-100 pickup, one star
1961 Ford Country Sedan wagon, three stars
1958 Chevrolet, one star
2.21
1962 Ford Galaxie convertible, three stars
2.22
unknown panel van (Ford?), two stars
2.23
unknown panel van (Chevrolet?), two stars
2.25
1959 Buick, one star
1958 Chevrolet Biscayne, one star
2.26
1961 Ford Falcon Futura, one star
2.27
1962 Ford Country Sedan, one star
1956 Ford Victoria, two stars
1955 Ford Fairlane Sunliner, two stars
2.28
1962 Ford Galaxie, four stars
1962 Lincoln Continental, two stars
1957 Dodge Sierra (?) station wagon, one star
2.30
ACF-Brill IC-41 (unknown year), three stars
2.31
1955 Ford, two stars