I had that problem with Sunshine Senegal and Trixie Meyers. These two birds literally fought over spending time on me, and each of them felt ONLY they should be on me. It turned into a huge fight between these two birds and Sunny lost the fight. Trixie monopolized the time for whenever she was out of her cage. Sunny literally got depressed, stopped eating, sat on a high perch when both the the birds were out and stared at me. Sunny lost interest in life and I thought she was sick and took her to the vet. Sunny was sick, she was depressed and thought I had picked Trixie over her as my favorite bird. My vet said the only way to solve it was to divide my day equally between them and to keep one caged while I spent one on one time with the other.
Trixie Meyers was a very light activated bird; more active in the morning and at noon, and as soon as the light decreased in the late afternoon and evening, she went to bed and would not interact. Sunny Senegal, however, had been with me much longer and was used to be not getting up (I worked nights) until three or four in the afternoon and then, on nights off, spending time with her in the birdroom until three or four in the morning. Therefore, Trixie got mornings after I got home from work until I went to bed on days I worked. Sunny got a brief greeting these days, a share of my breakfast for and hour, and then back to her cage. But when I got up from sleeping, I would greet Trixie, share my late lunch, and put her back in her cage, and then get Sunny out and spend one on one time with her until I went to work and left the house at ten PM. When I was off work, I spent the morning with Trix until two PM. Then a nap, and Sunny came out of her cage in the evening and I spent time with her until I got sleepy and back for another nap (usually three or four AM).
That is what I suggest to you. Partition your day into blocks of time for one on one activities with each bird. That way each bird gets your undivided attention. With Trix and Sunny, I could allow both of them out of their cages together in the mid-afternoon, and they wouldn't fight (if they did then someone was caged, usually the one who started it), so things got better with both birds. When Sunny and Trix were both busy doing other things, the cockatiels and lovies and budgies came to me for one on one attention. Pay attention to what goes on between your birds and make sure they are both happy.
