I am able to play chord progression in any key, but if I want to play by changing the KEY then it is difficult for me to play in the new key. So is there any easy technique to remember the chord conversion?
All chord progressions can be labelled by the degree of the chord within the scale. Most chord progressions will contain the I, IV and V major chords. They also may contain a ii, iii, or vi minor chord or a diminished 7th. Some chord progressions will contain other variants but every key has only certain type chords that can be derived from the notes in that key. And the type and degree is consistent across all keys.
You can label a chord progression according to where these scale degree chords occur in the progression. For example, the verses might be a I V vi IV progression and the chorus might be a I IV V progression.
So in any key you can use this format to identify which chords are used. If in key of A the I chord is A and the IV chord is D and the V chord is E and the vi chord is F#m etc. In the key of G the I chord is G the IV chord is C and the V chord is D and the vi chord is Em.
So once you reduce the chords in one key to the corresponding degrees of I, ii, iii, IV, V, vi, and diminished vii (or other variants which can occur), you can figure out which chords to play in any key.
There is a great and easy to read chart here Chord Progression Chart that shows all the chords for all the different keys. I keep this handy for transposing from one key to another without having to think about it.
Hope this helps.
Check out the Nashville Number System. I won't describe it here, as I believe it's been featured in other answers, and readily available through Google.
If - you're talking about transposing on guitar, if the original is played using only barre chords, then they can all be moved up by the same number of frets. Gets tricky moving down, sometimes, though, as the frets run out at the bottom!
Sure there's an easy way - you basically just use the alphabet! If your song is in A and you want to play in B - just "add 1" to each chord letter A->B, D->E, F#m -> G#m
It's not always so simple but in many cases this works just fine.
You'll also typically find you play in only a few keys - I rarely end up in anything other than C, G, A, or E and that you tend to use only a few chords (the famous 4 chords I IV V vi). I found I naturally learned to transpose these common chords so if a song in C is written C G Am F, and the band leader says "let's do it in E" I know that the minor chord is C#m "on autopilot.