It would be really hard to do BFL with no weights, or time for cardio. The simplist answer is to go to the library and get the book. Most of it is filled with success stories and motivation.
Also check the sticky at the top. It gives a link to pdf pages to print out. They do not tell you how to do exercises though, as there are no specific exercises to do. You work specific body parts. Lower body days you do quads, hamstrings, calves and abs. Upper body days you do chest, shoulders, back, triceps, then biceps. Three days a week you do cardio.
What makes it BFL is you do it pyramid style, basicaly doing 6 sets, with specific reps each set and raising resistance or weight each set. That is why it would be hard to do it without weights.
Best thing is to see if you can find a gym with child care, or someone to watch the baby for 1 hour 6 days a week. On lifting days you would spend about an hour working out, and on cardio days 20 min.
I have a baby at home too, along with a 4 year old, so I know how hard it can be to find time. What may suit you better is to find workout tapes that you can do while the baby is napping, or before bed. Yoga and Pilates are great choices and don't take up much room. You only need enough room to lay down. There are also books you can look into on exercises and yoga you can do with the baby. That could be fun for both of you