'at your convenience' vs 'to your convenience'

[Berawd]

I have always been mystified by the use of the word 'convenience' and more specifically whether one should use 'at your convenience' or 'to your convenience' in particular situations. Of course, one can always play it safe and use 'if it is convenient for you'. Can someone please enlighten me in what particular situations one can use correctly 'to your' and 'at your'?
Thank you.

[Conchita]

The commonly used phrase to mean 'when or as (rather than 'if') it suits you' is, 'at your convenience'.

Oh, and welcome to the site, Francis!

[Berawd]

Thanks for your welcome Conchita! I tend to agree with you when it comes to the commonly used phrase. However, we have a custom over here that whenever a person is invited to a social activity which involves the giving of gifts, the guest is sent a note with the invitation stating these exact words 'if it is at your convenience, monetary gifts are greatly appreciated'. Although the use of this phrase is used widely, for me it sounds funny. The proposition 'at' doesn't really seem right here. 'At your convenience could be more attributed to a time factor like saying, for example, 'when it is convenience for you' then saying whether it suits your pocket! Do you agree?

[Conchita]

I agree with your take on it -- the invitation note does sound unnatural. I'd rather say something like 'If it is convenient for you', or perhaps 'to your discretion', though the latter has a slightly different meaning and is a bit formal. The sentence could then read:

Monetary gifts are greatly appreciated and left to your discretion.