What sort of colours do you like? Maybe that's the best starting point to go with & you can build up a colour scheme from there? I've seen aqua/teal/mint green thrown around? You've already got greens now though so not sure if you'd want to go with that again?
If you did want to go down that path though something like
this could be easy on the eyes but still has the neon/bright green in it. I could easily see other neon colours working well with it too (E.G. yellow, orange, possibly pink & blue)
This could be another good one, & would just need neons added to it.
Here's a blue/green scheme which could also work well with some neon/bright shades
I feel like
food-related colour schemes or
sweets-related colour schemes would be good for you to go through & see if there's anything which jumps out at you. They seem to have a mixture of the softer shades with brighter ones. Some do have the Easter-feel too so you may need to do a little digging & exploring to get past that but I feel like there might be something there for you in one of those categories. My other suggestion would be to look up 'Citrus Colour Schemes' in Google Images as that could give you some nice choices too since citrus fruits come in some brightish/colourful shades
Keep in mind that we can try to combine colour schemes or alter them to meet your needs further so if there are any you feel are almost what you want we may be able to work with it still to reach something you can be happy with
This isn't exactly bright, but its colourful & doesn't make me think of Easter. Its sort of similar to the primary colour idea which was mentioned in here, without being too harsh on the eyes. For it I'd imagine a green board with the red/pink, blue, & yellow used more in the bar/link/buttons areas or a yellow/green board with the red/pink & blue used in the bar/link/buttons areas. We could probably brighten them up a little too?
Anyway, I'll let you all have a think & look around & see if there's anything you can find which you like