I have this problem also, allrv00. You also touched on what works for me ... once I am up and going I am ok.
Here is what helps me - when I am laying in bed in the AM and negative thoughts start, I think of one small positive reason to get up, which is usually a good cup of coffee.
Then I do something similar to what Jan1212 does and tell myself that these feelings usually pass and by mid-morning I will be better ... and I am. And I have something to look forward to later in the day or evening.
Another idea is to get up a little earlier than you need to and do something you like that sets a positive tone for the day ... do a spiritual reading, write in a journal, yoga, etc. - whatever moves you to a more positive place.
It gets better if you work on it ... at least is had for me.