Попробуйте так (элемент с классом .radio-block__bg-image нужно сделать фоном всего блока):
<div style="text-align: center;">
<div class="radiocontainer">
<div class="radio-block" style="background: url('cover.png') no-repeat;">
<img src="cover.png" class="radio-block__bg-image js-rotatable-image"/>
<div id="jquery_jplayer_1" class="jp-jplayer"></div>
<div id="jp_container_1" class="jp-audio-stream">
<div class="jp-type-single">
<div class="jp-gui jp-interface">
<ul class="jp-controls">
<li><a href="javascript:;" class="jp-play js-play-button" tabindex="1">Play</a></li>
<li><a href="javascript:;" class="jp-pause js-pause-button" tabindex="1">Pause</a></li>
<li><a href="javascript:;" class="jp-mute" tabindex="1" title="mute">Mute</a></li>
<li><a href="javascript:;" class="jp-unmute" tabindex="1" title="unmute">Unmute</a></li>
<li><a href="javascript:;" class="jp-volume-max" tabindex="1" title="max volume">Max volume</a></li>
</ul>
<div class="jp-volume-bar">
<div class="jp-volume-bar-value"></div>
</div>
<div class="jp-current-time"></div>
</div>
</div>
</div>
</div>
</div>
</div>
<script>
(function(){
const img=document.querySelector('.js-rotatable-image');
const playButton=document.querySelector('.js-play-button');
const cancelButton=document.querySelector('.js-pause-button');
const degreePerCall=1;
let isPlays=false;
let curDegree=0;
[playButton,cancelButton].forEach(function(node,i){
node && node.addEventListener('click',function(){
isPlays=!i;
});
});
requestAnimationFrame(function rotate(){
if(isPlays){
curDegree=(curDegree+degreePerCall)%360;
img.style.transform='rotate('+curDegree+'deg)';
};
requestAnimationFrame(rotate);
});
})();
</script>