Hmmm...
This is a difficult issue because I can't imagine when both sounds would be confused, but saying "pe'o" would sound strange; usually, we do that when "pero" is just a linking word, but here it is a main word in your sentence. On the other hand, stressing the "r" sound might make it closer to "perro", which would also cause a smile.
I can only advice you try pronouncing "d" with your tongue relaxing between your teeth (not behind them, as in English), and "r" with your tongue touching the roof of your mouth but not too close to your teeth. I think this way you'll manage to differentiate both sounds.