This answer has been heavily rewritten and rearranged to make it (hopefully) easier to read. The idea and rationale hasn't changed however I have changed (weakened) one of my assumptions as it seems it was to far fetched (I read it between the lines taking also some questions from comments as an actual state).
Further parts will provide explanation why I suggest this strategy, this is just a step by step idea how to solve the problem.
First establish why your Line Manager (LM) wants you to be in those meetings and discuss with Project Manajer (PM) what is his perspective (does he/she think it's needed?). It might be that it's about LM wanting to be up to date with the project status through you. Other option is that he thinks your participation in the project is crucial.
Arrange a meeting with both LM and PM and
If LM thinks your attendance is essential but PM not, try discussing the best way to keep track of the project status without your attendance to stand ups (if that's why LM wants you in the stand-ups) or how would it be best to have you in the meeting when you're really needed.
Either way bring up that most of the time you're not participating in the project and your everyday presence brings little to no value while costs plenty of your time and some of team time so it would be best if you joined the meetings only when there is a direct reason for it - either you do something for the project at that specific time or project team needs some information from you (which in most cases can be achieved in some other way).
If that fails but the time of the meetings is really outside of reasonable working hours, ask for rescheduling the meetings to some more convenient time.
If both PM and LM agree you're needed in the meetings and it cannot be recheduled that's probably all you can do. Always remember there is an atomic option if you really can't stand those meetings.
Be aware any other software development team you might join after leaving this one is likely to heave stand ups as well. They might only be in more convenient hours. On the other hand the project also doesn't last forever. If this is the only problem and the above suggestions don't help, I recommend you just try to hang in there until the project ends.
2. Working hours and meeting schedule
Are your working hours actually defined? If you work in environment anything like mine (rather standard for software development company/department) there is a large flexibility in your working hours. Yet usually there are rules when you have to be available for meetings (e.g. 9 a.m. - 3 p.m. or even 9 a.m. - 5 p.m.). If you have any meeting planned within that range of time you just have to accept that.
If the meeting is outside of that time you can request moving it to other timeframe. Yet since you're apparently not a key participant, there is a huge risk that this request will be rejected. Usually you can't do much about it anyway but that might become a point in discussion why you should attend in the meetings only when really needed.
If you don't have any strict availability hours but the meeting is in reasonable time (8 a.m. still has to be considered reasonable!) then again, there is little you can do about it. Effectively your flexibility is then limited but it does not excess in any way what an employer might require from you. If the hour is unreasonable due to e.g. time zones difference (for example the meeting is at 6 a.m. or 6 p.m.) this can again work as an excuse to attend only when your participation is really valuable.
Real life example:
I work in a project where every Monday and Friday we have a meeting at 4 p.m. Having flexible working hours I like being early at work and leaving early, meaning I usually leave at 4 p.m. But on Modays and Fridays I simply show up and leave an hour later. There is nothing I can do about that. Moreover the Monday meetings are often cancelled at the very last moment or even the host simply doesn't show. It changes nothing since when they happen I'm crucial to it.
3. Private stuff
Let's be plain about that. If you're within working hours your private stuff doesn't matter. Especially when we're talking about something planned upfront. Just accept it. Don't bring that on a table during a discussion or everything you'll get is a negative outcome. Look for other arguments that might support your case in discussion.
4. Value of the meetings
This is another topic that you need to weight very carefully and pick the right wording to avoid negative response.
Stand ups are often perceived as a waste of time by teams. There are several reasons for that, one of them is that people don't understand the purpose of that meeting. Second - they are led incorrectly and result in actual waste of time. If a stand up is run properly it should be a short meeting very efficient in exchanging information and putting everyone on the same page in terms who does what. It should also help to immediately address issues that happen during the project.
Yet what is important (I would even say critical in your case) - these are internal project team meetings. Apparently you're not part of the project team, just occasionally provide some service to them.
Stand ups should not serve as a means of providing the "external world" the status of the meeting. It actually makes those meeting less productive.
If the main reason why your manager wants you to attend those meetings is to keep track of the project status then you have a very strong case to discuss your attendance to those stand ups.
Since you're not a part of project team then according to Agile you should not attend those meetings unless there is a reason for that (e.g. you do something for the project at that time). It might be that your Line Manager (LM) wants to keep track of the project progress and uses your small involvement in the project as an opportunity to be "the inside guy". If that's the case, the best you can do is discussing with both LM and PM how to establish a good communication path so that your LM can be sure about the project status. If the project team uses some tools supporting project tracking (like JIRA, Rally or even Mantis or other Bug tracker), an access to such tool and some dashboards about the project status might do the trick without your involvement. Otherwise you might agree on some regular status meetings. Maybe there are some happening already, after all there should be some project status update for the sponsors. Other option might be some regular reports provided to LM.
If you are supposed to join the meetings because you're part of the project team, you should challenge it. If you provide only occasional service to the project there should be some agreed way to communicate when your involvment is needed. You should then attend stand ups while you're directly performing tasks for the project but only then.
You should first discuss that with the Project Manager (PM). He might be your ally here since your attendance to the meetings can render counterproductive.
5. Waste of time?
Anyway, avoid using the wording "waste of time" in the discussion with LM. Look at my answer so far - I use it really hardly. For a reason. Yet, if you insist on using this particular word, what you can do is bringing up another Big Word - LEAN. If there has been any attempts to introduce LEAN in your company you can bring it up claiming, that your attendance in the meeting is a waste according to LEAN. You should join only if it is a benefit for the project.