I understand this. I have struggled with depression as well, and have my own reasons for not wanting to get into therapy or take medications.
18 months ago I was actually suicidal (following a series of bereavements - I just couldn't make sense of the world any more, and it seemed far too painful - I couldn't bear the thought of losing anyone else, and thought I would rather die than have it happen again).
You can use LOA to combat depression, and very successfully, at least in my experience.
1. What I did was to affirm that I wanted to be happy. I didn't say "I am happy", as some people will advise - that was just too far from the truth, and my brain reacted against it. But wanting to be happy is the truth, so I could say that and not activate any resistances in my mind.
2. I also said that I was grateful for every moment of happiness that I experienced - and to reinforce the truth of that, I recalled every recent moment that I had felt happy, tried to re-experience the feeling, and said , "Thank you" and re-affirmed my gratitude for that feeling.
3. I also acknowledged that it is perfectly normal to sometimes feel down, and that I wouldn't get angry with myself if this did happen on occasion. Instead I decided that I would look at the issue that was bothering me, and see if I could do anything about it. If I could, then I did, otherwise I made a conscious decision to let go, and re-affirmed my desire to be happy, and my gratitude for every moment of happiness I experience (repeating steps 1 and 2 basically).
4. The other thing I found helpful was to repeat these affirmations while practising deep breathing - so, breathing deep into your belly, visualising your diaphragm moving down and allowing your lungs and belly to expand from the bottom upwards for the in-breath (count of 4) and then exhaling also from the bottom up on the outbreath (count of four). Trying to imagine that you can feel your blood (or energy or chi alternatively, if you believe in those concepts coursing through various parts of body, focussing on building that energy, also seemed to help (I think it just helped in terms of quietening the mind)
I hope that helps some.