Is there any meaning difference between these two sentences?
I was supposed to play.
I was supposed to be playing.
Yes, there are differences. How they differ really depends on the context, but I will give some examples to clarify.
(Unlike some languages, English isn't as strict about whether a tense grammatically indicates a specific aspect, nor whether a verb lexically does so. This complicates things by giving us more possibilities.)
"I was supposed to play." indicates either that someone expected the speaker to play on one occasion, or that someone expected the speaker to play for some amount of time. Here are two examples with more context:
"I was supposed to play baseball yesterday but it rained." We're thinking of "play" as a single activity within that day. (This is the perfective aspect, because we mainly care about the action being completed.)
"I was supposed to play football that summer, so I didn't join the baseball team." Here, we're instead thinking about many instances of playing as a reoccurring activity. If I say "I play baseball.", I mean it generally. I don't mean that I'm playing it right now.
Now, the second: "I was supposed to be playing." The simplest way (but not the only way) to think of this is that someone expected me to be playing now. Here's some context:
"My coach is angry because I was supposed to be playing baseball right now." (We planned or agreed that I would play, and I'm not doing it now.)
Continuous tenses are funny in English, because we can use them for multiple meanings. A second use of "playing" can emphasize activity during a time period (similar to "I play baseball every Friday." but emphasizing the activity more, as in "He never stops! Every Friday, he's outside playing baseball!"). This can be for several reasons, but here's one example of that, used to indicate repetition: "Why are you spending your summer at home!? You're supposed to be playing baseball!!"
We also often use a continuous tense to emphasize that something is temporary, even if it happens over a long period of time. "I play baseball a lot, but I hurt my arm and I'm playing soccer/football until I feel better." To use this with "supposed to": "The baseball team didn't have enough players, so I'm supposed to be playing baseball this week, but after that I'll play basketball again."
What makes this even more complex is that a continuous tense "to be playing" can sometimes be used to describe the future. For example:
"I'm playing baseball with them next week." This is a more natural way to say "I will play baseball with them next week.", with a feeling that it's already planned and that there is some "momentum" leading toward the playing.
I can use the infinitive form of this, "to be playing", with "supposed to" like this: "I'm supposed to be playing baseball with them next week, but I'll call them to be sure." Often, this form is used when I've planned or arranged an activity with other people.
So, to summarize:
"I'm supposed to play..." can mean that I'm supposed to play on one occasion, or several times across a longer time.
"I'm supposed to be playing..." can mean that I'm supposed to be actively playing at this second, can mean that I'm playing over a longer time (but emphasizing activity, repetition, or that it's temporary), or that it will happen in the future (often with a plan involving other people).
WikiDiff.Com says that "to play" mostly means:
"To act in a manner such that one has fun; to engage in activities expressly for the purpose of recreation or entertainment."
LearnEnglish-Online.com says that:
It is better to use a gerund as the subject of the sentence. An infinitive is very formal and doesn’t sound very good. It can sound poetic, philosophical, or classical literature.
It also says that:
Deciding between a gerund and an infinitive as objects is much more difficult than subjects. You must learn which verbs are followed by gerunds, infinitives, or both. The list below shows you the differences.
It gives a list of verbs that can only be followed by a Gerund:
Admit,anticipate,appreciate,avoid,can’t help,complete,consider,delay,deny,discuss,dislike,don’t mind,enjoy,finish,get through,give up,imagine,keep,keep on,mention,mind,miss,postpone,practice,quit,recall,recollect,recommend,resent,resist,risk,stop,suggest,tolerate,and understand.
And verbs that can be followed only by an Infinitive:
Agree,appear,arrange,ask,care,choose,claim,consent,decide,demand,deserve,desire,fail,guarantee,happen,hope,know how,learn,manage,tend,offer,prepare,promise,refuse,seem,struggle,swear,volunteer,wait,want,and wish.
And verbs that can be followed by either a Gerund or an Infinitive:
Can afford,allow,attempt,can bear,begin,can’t stand,continue,dread,expect,forget,go,hate,hesitate,intend,like,love,neglect,plan,prefer,pretend,regret,remember,start,stop,threaten,and try.
As we can see "suppose to" isn't in that list but I found this interesting document that gives a hint:
I agree with that. And there is another notice:
BE + INFINITIVE is used to:
It's also widely known that where you can use a Gerund with a verb it's more common to do so in especially informal English than use a To+Infinitive.
Based on what we have the difference between the 1-st and the 2-nd sentence is that:
The 1-st "I was supposed to play" sentence conveys the idea of "to play" to be an entertainment. The stress here falls on the idea in general, the activity. It may also mean that "I was supposed to do that whether I wanted to or not". Besides that it can also mean "I was supposed to [play] and not do something else".
The 2-nd "I was supposed to be playing" sentence conveys the idea of it being a play or a job or some sort. Besides that it also conveys the idea of it being a preference or something really liked or enjoyed. It is more informal and pictures a person not being happy about it. The stress here is on the action from the activity and not the activity.
Basically, while both sentences might likely have the very difference I mentioned they are both equal and practically have very little to no difference at all!
Edit: This answer is incorrect. I leave it here in case others later have the same confusion between present participles and gerunds. Sometimes grammatical labels are especially hard to learn in your native language!
The two sentences are very nearly synonymous.
The gerund form of a verb is when you end it with -ing, and it very often allows the verb to be used as a noun. So, if you want to sleep, you would like to be sleeping.
Some more resources about gerunds: