The sentence is not referring to any time past, present of future. It's just referring to an imaginary condition which has never existed and seemingly will never exist. Still, the sentence and other sentences of this type are said and spoken. So what can we say about their nature? Which tense are they, what type are they? Their clauses, etc.
Were is the plural past tense form of be, used here in a counterfactual conditional idiom construction that is given various names, including "subjunctive", which often apply to other European languages, though not to English.
In fact, however, tense is not what you need to know here. Tense only has to do with time -- past and present only in English -- and the important thing about this construction is not when it occurs, but whether it occurs at all. And it doesn't; nothing happens. That's what counterfactual means.
So, in essence, there is no tense involved. Especially since the second clause uses the modal auxiliary could. Modals are defective verbs and are not inflected; therefore they can be said either to be always in the present tense, or to have no tense at all, depending on how you define "tense"; take your pick.
It's true that there are certain uses of modals that retain some of their original preterite morphology, e.g, present can and preterite could in
But there's no "past" at all in
which are formed from historically preterite modals (could, might, would, should, must) instead of historically present ones (can, may, will, shall).
They're all idiomatic now. It's a mistake to expect any consistent semantic or grammatical regularity from modals, especially if there are negatives lurking about.
If I were is in the past subjunctive. It is used for hypotheses.
Then I could, like then I would be able to, is construed to be in the conditional. However, morphologically, could is the past tense of the modal can.
The verbs in this sentence are vestiges of a subjunctive used in English to indicate conditions contrary to fact. We indicate this usage by using the plural form, where it exists, of the past tense.
Were is the plural past tense of to be. Could is the past tense of can (no singular/plural distinction exists).
Example: I have gone to the store to buy milk. If I had gone to the store to buy milk...