I found directions for a vertical buttonhole,
Work to the position of the buttonhole, then divide the work by dropping the old yarn, joining in another ball of yarn and wroking to the end of the row.
For the next few rows, until the buttonhole is the required depth, continue to work each side separately so that the band is divided into two parts.
To close the buttonhole, work across the whole row with the original end of yarn. Strengthen the top and bottom of the buttonhole with a stitch using the spare ends of yarn.
This might be a problem in the round, but maybe for the rows of the buttonhole you could work back and forth and then continue in the round when it's done.