Yes there is.
I just got honor level 2 a few hours ago after 3 months.
The time passed is kind of misleading. For reference I was honor level 0, and it took approximately 235 Summoner's Rift games and about 8 ARAM matches.
My tips are as follows.
- Don't mute all.
- Honor after every match.
- Play what you're comfortable playing.
- Play a lot of matches.
- Drop your friends. Play solo.
- Avoid ranked, especially at this time.
I've seen a lot of advice thrown around on the boards that doesn't align with my experience. I'll just go through them. We don't really know what exactly speeds up honor progression or slows it down, so this is subjective. Keep that in mind.
In my opinion you shouldn't be afraid of the chat, especially with this time crunch. If you're being positive most matches, then that's good enough. I wasn't exactly friendly all the time, but I never told anyone off if they were being disgusting. I actually never muted anyone. I just ignored them or laughed about it.
I've also seen people say "LEL play support and get mad honors bro." First of all, unless you're playing something cheesy in low ELO, appreciation is hard to come by for most supports as they don't often make flashy plays and their impact on the game isn't front and center either because Riot doesn't make certain stats a priority, or they simply can't because utility is hard to show stats for. Unless you do something extraordinary to save the game, most of the team won't notice you.
Normally the ADC will honor you, but that's mostly because you always remember the person you survived a 4 man gank with while your jungler AFK farms.
[sg-lulu]
It is just better to play what you're good at to avoid frustrating experiences that come with learning new patterns. You're already grinding due to the honor system, so don't make it stressful.
More importantly though the honors you receive don't really impact honor progression that much in my opinion. I never notice a difference when I would have long streaks of awesome games and got the majority, if not all, honors compared to times when I was mediocre and got maybe 1 honor at most. It is crucial that you honor people after every match though. I really noticed progression after I started doing that.
Another mistake I made was playing with 3-4 other people for much of September. The honors you get from friends and you give to friends don't make much of an impact.
Finally the honor pop-up wasn't instant for me either. I played a few games, went out, came home, opened the client, and there it was a notification that I unlocked honor level 2.
Anyways, hope this helps and good luck.