Technically, ηὐχόμην is deponent which is a middle conjugation that is translated as active. The imperfect tense is an incomplete action. It's up to the translator to interpret whether it is iterative (periodic), inceptive (the beginning of the action), durative (a constant, ongoing action), etc. Translation of the imperfect is usually accompanied by the helping verb "was."
Tense provides insight into the temporal aspect of the verb.
Voice provides insight into the object of the action.
Mood provides insight into the reality of the situation.
Person provides insight into who is performing the action.
Since Paul used the imperfect, middle-passive (deponent), indicative, 1p singular, this means that it was him who was performing the action (person).
Indicative (mood) is a statement of reality and not some future hope or wish (which will be important when using the looking at the verb εὔχομαι).
The middle deponent (voice) which is tempting to translate as a middle reflexive but that would render "I was wishing for myself that ..." In the case of a deponent we render the verb as an active "I wish." We also see that αὐτὸς is placed in a reciprocal configuration just a few words later which would make a middle voice verb out of place, and give us a nonsensical translation.
The tense, as mentioned above, provides temporal aspect to the verb --- when it happened. Also as mentioned, imperfect indicates that the action is not yet complete (as of the time of writing).
Now, with this verb it is most likely that the focus is on Paul performing the action, given the indicative mood. It really happened that he was wishing. If the focus was on the curse, then he probably would have used the subjunctive or even optative mood which would indicate a level of uncertainty about the reality of the verb. He probably wouldn't have even used εὔχομαι if this was the case. The real sticky part of this, as Bob Jones identified, is the use of the imperfect. So, is it iterative, durative, inceptive? We must make a decision.
Durative would render "I was constantly wishing"
Inceptive would render "I began wishing"
Iterative would render "I was regularly wishing"
I prefer "I was wishing" because it holds truest to the parsing and separates the theological endeavor from the translation (which does require a degree of reading one's theology into the text - but I seek to minimize that at the translation step).
My guess is that the later use of δὲ which links what follows with what preceded (usually through antithesis) leads translators to use "could" because it cedes priority the the will and word of God which is not dependent on the object of a curse or on the wishes of a person.