Recently I have been trying to learn to pronounce the voiced th properly.Is it a correct way of pronouncing it by saying "d" with my tongue between my teeth?I know that this is not the canonical way,but to me it seems that this is a much easier way to do it and it is close to the way the natives pronounce it.
Not quite. It is indeed interdental (tongue between the teeth), but for most English speakers it is quite distinct from even an interdental /d/, because it is a fricative, not a stop.
In stops, like /d/ and /p/, there is a moment when the tongue or lips actually block the airflow, and there is a complete break in the sound. In fricatives like /s/ and /v/, there is never this complete break - the tongue or lips never quite meet, but the sound is formed by their coming close together.
If you can say the unvoiced th, then you already know what to do with your mouth to say the voiced th. Of course, just make the unvoiced th voiced; remember to let your vocal chords hum while saying it. Voicing is the only significant difference in the two. Here's more about voiced and unvoiced sounds.
Try this: say the "uh" sound continuously (the schwa). As you're saying it, very slowly move your tongue forward. As your tongue gets very close to your teeth, you'll hear the sound change. And you might feel your tongue vibrating slightly. That's the voiced th. Practice it by saying words like other, mother, and brother, then practice words like the, then, that, and there.
Some Americans do pronounce the th as a D, but that is definitely not standard, and I don't recommend saying it that way.