Rattling noise coming from my passenger side of my engine

I noticed earlier last week that when I start my vehicle I hear a rattling noise kinda hard to explain unless you actually hear but car but when I start it it rattle for a couple of seconds and then I i put it in drive and I accellerate just a little to get my car to move it more rattling as well yet agin for a couple of second then it stops I went to a mechanic and they said I need to replace my tension pulley so I replaced that they said it would stop to rattling well it didnt so my husband looked at my spark plugs they were bad I replaced all my spark plugs as well as my valve cover gasket because I found out I had oil on my plugs luckily I found that out right when the leak happened I have plenty of oil in my car so we are stumped as to what my problem with my vehicle is I also had my motor mounts check out by 2 mechanic shops my motor mounts are fine they are suggesting get a diagnostic test unfortunetly I dont have 89 bucks to get that done do you have any idea what may be the problem