Neither would VERB or used to VERB is appropriate here.
These constructions are employed to speak of actions which were habitual or repeated over a fairly long period of time.
When we were living in Jersey John and I used to go to the casino every weekend; I never played myself, but I would keep John's chips for him.
In your example, however, your friend is speaking of what he was doing on a single occasion. He is describing what he was doing at the time his uncle saw him. Since that action—keeping John's coins—was already 'in progress' at the moment when his uncle saw him, he should employ the progressive construction, exactly as you do in the previous sentence:
You: What if he did see you in the casino? —it doesn’t mean you were playing there. You were just accompanying John.
Your Friend: I was keeping John's coins on the table. He saw that, and thought I was playing.
However, it is possible for your friend to use would here in a different sense: to indicate that what his uncle saw and concluded is not something which your friend knows to be a fact but is something which your friend infers from the situation:
Your Friend: I was keeping John's coins on the table. He would have seen that, and [would have] thought I was playing.
Note that this employs what I call the 'sham perfect' construction with the past-form modal + have + past participle. This is not a 'true' perfect but the perfect construction employed to mark past reference in a context which would otherwise be ambiguous.