The same challenge can be found with musicians learning keyboards as they have to learn how to coordinate both left and right hands playing together.
To accomplish this, students are given pieces that progress from easy to hard and they advance as they are ready. The key here is to break down each part to beats whether you are singing one part and playing guitar or drums or keys on the other.
Learn both parts then when you feel comfortable with each part, you can begin to combine them. Start with a very slow tempo until you have it and then pick it up until you are ready for the desired tempo. This all boils down to practice. If you get stuck, remember if you can learn one part, you can learn both, if you learn both parts, you can learn to play them together. Like rubbing your tummy counter clockwise with your right hand while circling your head clockwise with your left hand at the same time.
Another strategy to get really good at this is to swap parts, try playing the drum part with making sounds with your mouth, and play the melodic beats with your drums. Of course this will be way easier to swap parts when both instruments can play melodic content.
Yet another strategy is to practice poly rhythms with two hands. One hand plays three beat pattern say accent plus two more beats while the other plays a five note pattern say accent plus one beat then accent again followed by two more beats (3 against 5). You can make up as many combinations as you like to make it more challenging. This will help teach your hands to move more independently.
Here is an example of a poly rhythm exercise from a pianist eager to get better:
One last thing, since you mentioned voice, make sure you take a breath before each phrase and this may help to keep time as well.