Getting bigger shoulders takes work, in and out of the gym. Training at home is a slight obstacle, but this doesn't mean it cannot be overcome. Your best bet is to invest in a set of strong resistance bands with handles. These make good, affordable home tools that can be used to work any part of your body. Couple resistance band exercises with body weight exercises, and you will be well on your way to achieving your goal.
Perform a set of pike pushups. Lie on your stomach with your hands and feet approximately shoulder width apart. Steadily push yourself off the floor by extending your arms and raise your hips in the air. Push your weight back toward your heels and form an inverted angle with your body. Maintain this alignment as you bend your elbows and lower yourself down. Stop when your forehead is an inch above the floor, push yourself back up and repeat. Perform 10 to 12 reps and four to five sets of this and all subsequent exercises.
Stand with your feet shoulder-width apart to do shoulder presses with the bands. Hold a handle in each hand and stand on the middle of the band. Position your hands right above your shoulders with your palms facing forward. Push the handles straight above your head and move your hands together. Hold for a second, lower the handles back down and repeat.
Execute a set of Hindu pushups. Assume the starting pike pushup position and look backward. Lower your body down toward the floor by bending your elbows and swoop forward as if you were crawling under a fence. Keep your hips just above the floor when you do this. Rise up and arch your back as you fully extend your arms. Hold this position for a second, then move back to the starting position by going the opposite direction. Alternate back and forth between each position.
Utilize a wall to do handstand pushups. Crouch down in front of the wall and carefully place your feet on it. Walk your feet up the wall as you walk your hands backward. Stop when your body is straight up and you are facing the wall. Position your hands about shoulder width apart and bend your elbows to lower yourself down. Stop when your head is about two inches from the floor, push yourself back up and repeat.
Grab the handles of a band to do alternating lateral and forward raises. Stand on the center of the band and hold your hands right in front of your thighs with your palms facing each other. Lift your arms in the air to your sides until they parallel the floor and lower them back. Raise them up in front of your body until they parallel the floor and lower them down again. Alternate back and forth with each position. Keep a slight bend in your elbows throughout.