Does this rotate so that one week you'll work a Monday and the following week you'll skip the Monday? Or do you work something like a 12-hour Monday, then a 24-hour Tuesday, then a 12-hour Wednesday night and have Thursday-Sunday off?
Regardless, if the days to nights transition isn't gapless then you should be able to fit in some training as you adjust your body's timeclock to the new time schedule. I used to work a job several decades ago where they could work you any shift as long as they gave you 8 hours between shifts, so I might work Mon-days, Tues-swing, Wed-grave, Thurs-swing, Fri-days, or the following week it might be Mon-Wed-days, Thurs-graveyard, Fri-swingshift. Really sucked as you couldn't plan anything for the week except on a day-by-day basis. After two years I quit that company and found a job with a more regular work schedule. But during that time I did bicycle a lot and basically snagged any time I felt like riding and went for a ride regardless of what time of day or night it was. The time of day would often determine what routes I took.
Someone can probably provide you with a workable training schedule if you provide a more specific work schedule to build around. It can be done, but there will be comprimises.