There are two ways to propagate miniature roses, either by cuttings or by seed. Cutting will give you reproductions of your favorite varieties, but don't propagate patented varieties in this manner for resale. Seed however, gives rise to a variable lot of plants which are easily matured under lights.
Take 3-inch cuttings during August or September from new growth. Cuttings you get from old wood are hard to root. Choose strong growing shoots. Dip the base of the cutting in a hormone powder like Rootone. Slip in numerous cuttings in a 6-inch bulb pan. You could also plant them separately in 2-inch pots of vermiculite or a mixture of 2 parts gritty sand (or perlite) to 1 part of peat moss. Stick the cuttings about an inch deep. If leaves begin to wilt, mist them frequently using tepid water. Place about 12 inches from the lights. Cuttings normally root in approximately four weeks. Transplant rooted cuttings to 2-Inch pots of sterilized soil.
Seeds of baby roses (Rosa polyantha nana) can be obtained from several sources. There is also a pre-seeded planter on the market that would give you dozens of these small roses. Seedlings are not generally fully double varieties, but they would bloom in seven to ten weeks from the time seeds germinate, generating single and semi-double flowers in shades of white, pink, and rose.
It is unclear if any firm offers seed of the fully doubles. You may be able to manage in making your own plants produce seed by taking out pollen from one flower and putting it on the pistils of another. If you are unable to find pollen on any of the doubles, use some from one of the baby polyanthas. You have to make dozens of pollinations to obtain seed from the named varieties.
Miniature rose seeds are pressed into any starting medium and covered lightly. A few would germinate in two or three weeks, but it could take 2 or 3 months for the whole batch. You may try adding the seed to half an inch of water in an ice tray and put it in the freezer. Remove in two weeks and plant the seed in peat moss and sand, or your favorite seed-starting medium.