Wow that is a ****ing loaded question dude. I'm not if anyone who would be reading this forum is really qualified to adequately answer it.
That said, it's an interesting problem and I'll give you my best (purely speculative) answer based on my current knowledge of biology.
From what I can find on Cyclobenzaprine, it appears the drug action effects your brain rather than your muscles. Which to me means it's not going to really have any effect on muscle growth or development, aside from atrophy due to possible under use.
Which, indirectly, WILL cause your muscles to not grow as quickly. The drug also seems to inhibit motor unit recruitment. This means it's very likely someone on this drug isn't going to be able to lift as much weight as someone not on the drug. Which would make sense, considering it's a muscle relaxant. Lifting lighter weights = not as much growth as lifting heavier weights.
That said, this all might be meaningless because...
FLEXERIL should be used only for short periods (up to two or three weeks) because adequate evidence of effectiveness for more prolonged use is not available and because muscle spasm associated with acute, painful musculoskeletal conditions is generally of short duration and specific therapy for longer periods is seldom warranted.
(from
http://www.rxlist.com/flexeril-drug.htm. Flexeril is a marketed brand of Cyclobenzaprine.)
Two or three weeks out of the gym isn't going to kill you. Minor, minor setback, assuming the rest of your program is spot on.
Of course, I don't know how you, personally, plan on using the drug, so beyond this I really can't comment, but it doesn't seem like you'd be on the drug too long.
That said, you have the usual laundry list of side-effects that come with every medication nowadays. Amongst those common to Cyclobenzaprine appear to be numbness, loss of motor coordination, stroke, heart attack, heart irregularities, lung collapse, on and on and on. Yes, all of those will heart your progress in the weight room

Of course we really can't say which ones you'll get and which ones are on there only because their lawyers are covering their ass.
Tramadol appears to be an analgesic that functions entirely on the brain, so I don't think that's going to do anything to your muscles either.
Alright there's the long answer, let me give you the short ones.
I was wondering what sort of effect these types of drugs will have on your workouts.
You're not going to be able to lift as much weight.
Specifically, will taking a muscle relaxer like cyclobenzabrine affect your muscle growth?
Only because you probably won't be able to lift as much weight. Otherwise, nah.
I know morphine will lower testosterone, but I haven't seen anything about Tramadol? What sort of effects will it have on the gains I am shooting for in the gym and with my diet?
I've never heard of a link between Testosterone and Morphine. Tramadol interacts with your body very differently than does morphine, so it's entirely possible that it won't be a problem.
Anyways, why are you getting on these drugs? Seems like if you actually have a reason to be using them, the thing you are trying to get relief from would be quite a severe hindrance to you in the gym as it is.