From a propagation book:
"There is no one best way to root a magnolia cultivar. Some species, such as
M. soulangeana and M. stellata, are commercially propagated by leafy softwood cuttings. Cuttings may be taken from late spring to late summer after terminal growth has stopped and the wood has become partly matured.

With M. stellata, 6 to 10 cm (2 to 4 in) softwood leaf-bud cuttings are wounded on the opposite side of the bud and the leaf blade is reduced 50 to 60 percent. The cutting is treated with a 8,000 ppm IBA talc or quick-dip (260).

M. stellata can also be rooted using four- to five-node semi-hardwood cuttings. The cuttings are taken in July to early August (Canada), the basal leaf is stripped, and the cutting is quick-dipped in an ethanol-based IBA (5,000 ppm) (218).

Leafy cuttings of M. grandiflora (with two to four leaves per cutting) are taken from late spring to late summer. Terminal buds should be hardened and not initiating new growth. Wounding can cause rotting, but enhances rooting in some cultivars. Auxins are needed to root M. grandiflora. Generally, a range of 3,000 to 8,000 ppm IBA, or combinations of K-IBA and K-NAA, give best results; cultivars are treated with as little as 1,000 ppm to a high of 15,000 ppm auxin combinations (200). M. grandiflora root best with mist under warm conditions, i.e., a bottom heat of 24°C (75°F), minimum 16°C (60°F) in winter (200).

With M. grandiflora there is considerable cultivar variation in rooting. Brown-black cultivars are harder to root, with the hairy felt on the leaves that makes moisture control more difficult. Other reports indicate that semi-hardwood cuttings root well when quick-dipped in 5,000 to 10,000 ppm NAA in 50 percent alcohol (123). Cuttings should be rooted early enough in the season so that some resumption of growth will occur before fall, which will allow them to survive through the winter. In Scotland, the leaf blade of leafbud or nodal-tip cuttings is partially trimmed to reduce transpiration, save propagation space, and allow sufficient air circulation; cuttings are treated with 3,000 ppm IBA in talc or a 1,000 ppm quick-dip, and propagated under mist with a basal rooting temperature of 18°C (64°F) (121).

In South Carolina, M. grandiflora ‘Little Gem’ are stuck in August and rooted by February of the next year. Cuttings are maintained at an initial 35°C (95°F) air temperature [minimum 16°C (60°F) bottom heat in late fall/winter], single wounded, and quick-dipped in 5,000 ppm IBA 2,500 ppm NAA (200). In
Mississippi, 13 cm (5 in) cuttings of M. grandiflora ‘Little Gem,’ ‘Red Robbins,’ ‘D. D. Blanchard,’ ‘Claudia Wanamaker,’ ‘Green Giant,’ and ‘Bracken’s Brown Beauty’ are taken in mid summer. Cuttings are wounded on 2 sides, about 5 to 7 cm (2 to 3 in) along the cutting base with a potato peeler. The cuttings are then given a quick-dip of 2,500 ppm K-IBA or equivalent IBA concentration of Dip’N Grow (31), then propagated at near 100 percent relative humidity at 38°C (100°F).

M. acuminata have uncommon yellow flowers but are difficult to propagate. Terminal cuttings had greater rooting when collected 5 to 7 weeks after budbreak and treated with 16,000 to 30,000 ppm IBA talc (376).

M. virginiana ‘Santa Rosa’ (Santa Rosa sweetbay) can be propagated from semi-hardwood cuttings (tips of first-order laterals) trimmed to 10 to 15 cm (4 to 6 in) with leaves removed from the lower half of the cuttings and the remaining leaves cut in half perpendicular to the midrib (186). A 5,000 ppm quick-dip of IBA enhanced rooting of cuttings."

American magnolia (grandiflora) is hard to root from cuttings. It is better to root through air layering. Or bend the lower cane and try to layer that way.

The deciduous Asian magnolia is easier to root from cuttings.